{"id":13866,"date":"2021-05-27T02:33:02","date_gmt":"2021-05-26T21:03:02","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=13866"},"modified":"2022-01-25T01:40:38","modified_gmt":"2022-01-24T20:10:38","slug":"02-02-00","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/02-02-00\/","title":{"rendered":"02.02.00 &#8211; \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link\" href=\"https:\/\/drive.google.com\/uc?export=download&amp;id=1PxRuicUvANdNJDDmBBZ6zFnqgh8d7hG8\" style=\"border-radius:15px\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n<ul class=\"has-text-color wp-block-list\" style=\"color:#ff0000\"><li><strong>\u0dc3\u0d82\u0dba\u0dd4\u0d9a\u0dca\u0dad \u0d9c\u0dab\u0dd2\u0dad\u0dba I (\u0dc1\u0dd4\u0daf\u0dca\u0db0 \u0d9c\u0dab\u0dd2\u0dad\u0dba) \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dad\u0dca\u200d\u0dbb\u0dba\u0dda B \u0d9a\u0ddc\u0da7\u0dc3\u0dda (\u0dbb\u0da0\u0db1\u0dcf \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1) 11 a)  \u0d9c\u0dd0\u0da7\u0dbd\u0dd4\u0dc0\u0dda \u0d85\u0da9\u0d82\u0d9c\u0dd4 \u0dc0\u0db1\u0dca\u0db1\u0dda \u0db8\u0dd9\u0db8 \u0db4\u0dcf\u0da9\u0db8\u0dda \u0d85\u0da9\u0d82\u0d9c\u0dd4 \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dcf\u0db1\u0dca\u0dad \u0dc0\u0dda.<\/strong><\/li><\/ul>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile has-background\" style=\"background-color:#c9cfd8;grid-template-columns:31% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"267\" height=\"400\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/08\/7550831.jpg\" alt=\"\" class=\"wp-image-25802 size-full\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/08\/7550831.jpg 267w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/08\/7550831-200x300.jpg 200w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/08\/7550831-150x225.jpg 150w\" sizes=\"(max-width: 267px) 100vw, 267px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p>\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0db4\u0dd2\u0dc5\u0dd2\u0db6\u0db3 \u0dc3\u0d82\u0d9a\u0dbd\u0dca\u0db4\u0dba 17 \u0dc0\u0db1 \u0dc3\u0dd2\u0dba\u0dc0\u0dc3\u0dda \u0daf\u0dd3 \u0dc0\u0dbb\u0dca\u0db0\u0db1\u0dba \u0dc0\u0dd2\u0dba. \u0db8\u0dd9\u0db8 \u0d9a\u0dcf\u0dbd\u0dba\u0dda \u0daf\u0dd3 Ren\u00e8 Descartes (1596 &#8211; 1650) , \u0d94\u0dc4\u0dd4\u0d9c\u0dda Geometry (1637) \u0d9a\u0dd8\u0dad\u0dd2\u0dba\u0dd9\u0dc4\u0dd2 \u0db6\u0ddc\u0dc4\u0ddd \u0d9c\u0dab\u0dd2\u0dad\u0db8\u0dba \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dad\u0dcf&nbsp; \u0daf\u0dd0\u0d9a\u0dd2\u0dc0\u0dd3\u0db8\u0da7 \u0db8\u0dd9\u0db8 \u0dc3\u0d82\u0d9a\u0dbd\u0dca\u0db4\u0dba \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dcf \u0d9a\u0dbb \u0dad\u0dd2\u0db6\u0dda. \u0d91\u0dba\u0dd2\u0db1\u0dca \u0dc0\u0dc3\u0dbb 50\u0d9a\u0da7 \u0db4\u0db8\u0dab \u0db4\u0dc3\u0dd4\u0dc0 Gottfried Wilhelm Leibniz (1646 &#8211; 1716) \u0dc0\u0dd2\u0dc3\u0dd2\u0db1\u0dca \u2018function\u2019(\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba) \u0dba\u0db1 \u0db4\u0daf\u0dba \u0dc4\u0db3\u0dd4\u0db1\u0dca\u0dc0\u0dcf \u0daf\u0dd9\u0db1\u0dd4 \u0dbd\u0dd0\u0db6\u0dd3\u0dba.<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0dc4\u0dd0\u0daf\u0dd2\u0db1\u0dca\u0dc0\u0dd3\u0db8<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>x \u0d9a\u0dd4\u0dbd\u0d9a\u0dba\u0dda \u0d91\u0d9a\u0dca \u0d91\u0d9a\u0dca \u0d85\u0dc0\u0dba\u0dc0\u0dba \u0d9a\u0dd2\u0dc3\u0dd2\u0dba\u0db8\u0dca \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dba\u0d9a\u0dca \u0db8\u0d9c\u0dd2\u0db1\u0dca y \u0d9a\u0dd4\u0dbd\u0d9a\u0dba\u0dda \u0d85\u0db1\u0db1\u0dca\u200d\u0dba \u0d85\u0dc0\u0dba\u0dc0 \u0d85\u0db1\u0dd4\u0dbb\u0dd4\u0db4\u0dab\u0dba \u0d9a\u0dd9\u0dbb\u0dda \u0db1\u0db8\u0dca \u0d91\u0dc0\u0dd0\u0db1\u0dd2 \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dba\u0d9a\u0dca \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0dbd\u0dd9\u0dc3 \u0dc4\u0dd0\u0daf\u0dd2\u0db1\u0dca\u0dc0\u0dda.<\/li><\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong><span style=\"color:#304170\" class=\"has-inline-color\">\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a \u0dc0\u0dc3\u0db8 , \u0dc3\u0dc4-\u0dc0\u0dc3\u0db8 \u0dc4\u0dcf \u0db4\u0dbb\u0dcf\u0dc3\u0dba<\/span> <\/strong><\/h4>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp; x = { 1,2,3,} \u0dba\u0dd0\u0dba\u0dd2\u0daf<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp; y = { 1,2,3,4,5,6,7,8,9,} \u0dba\u0dd0\u0dba\u0dd2\u0daf \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp; x \u0dc4\u0dcf y \u0d9a\u0dd4\u0dbd\u0d9a \u0d85\u0dad\u0dbb \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dba\u0d9a \u0d8a \u0dc3\u0da7\u0dc4\u0db1\u0d9a \u0daf\u0d9a\u0dca\u0dc0\u0db8\u0dd4. . f = x<sup>2 &nbsp;<\/sup>\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0dc3\u0dbd\u0d9a\u0db8\u0dd4.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/image-29.png\" alt=\"\" class=\"wp-image-13869\" width=\"328\" height=\"321\" \/><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>x \u0dc4\u0dd2 \u0d91\u0d9a\u0dca \u0d85\u0d9c\u0dba\u0d9a\u0da7 \u0d85\u0db1\u0dd4\u0dbb\u0dd6\u0db4 y \u0dc4\u0dd2 \u0d91\u0d9a \u0d85\u0d9c\u0dba\u0d9a\u0dca \u0db6\u0dd0\u0d9c\u0dd2\u0db1\u0dca \u0db4\u0dc0\u0dad\u0dd2\u0db1 \u0d85\u0dad\u0dbb x \u0dc4\u0dd2 \u0dc3\u0dd0\u0db8 \u0d85\u0dc0\u0dba\u0dc0\u0dba\u0d9a\u0da7\u0db8 \u0d85\u0db1\u0dd4\u0dbb\u0dd6\u0db4 \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0db6\u0dd2\u0db8\u0dca\u0db6 y \u0dc4\u0dd2 \u0db4\u0dc0\u0dad\u0dd3. \u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf \u201cf \u201c \u0dba\u0db1\u0dd4 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0db6\u0dc0 \u0db4\u0dd0\u0dc4\u0dd0\u0daf\u0dd2\u0dbd\u0dd2 \u0dc0\u0dda.<\/li><li>\u0db8\u0dd9\u0dc4\u0dd2 f \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0dda \u0dc0\u0dc3\u0db8(Domain) x \u0d9a\u0dd4\u0dbd\u0d9a\u0dba \u0dc0\u0db1 \u0d85\u0dad\u0dbb \u0d91\u0dba \u201cD<sub>f <\/sub>\u201c&nbsp; \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0dc3\u0d82\u0d9a\u0dda\u0dad \u0d9a\u0dbb\u0dba\u0dd2.<\/li><li>\u0db8\u0dd9\u0dc4\u0dd2 y \u0d9a\u0dd4\u0dbd\u0d9a\u0dba \u0d91\u0dc4\u0dd2 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0dda \u0dc3\u0dc4-\u0dc0\u0dc3\u0db8 ( Co-Domain )\u0dc0\u0db1 \u0d85\u0dad\u0dbb \u0d91\u0dba \u201cC<sub>f <\/sub>\u201c \u0dbd\u0dd9\u0dc3 \u0dc3\u0d82\u0d9a\u0dda\u0dad \u0d9a\u0dbb\u0dba\u0dd2. \u0d91\u0db1\u0db8\u0dca \u0dc3\u0dc4\u0dc0\u0dc3\u0db8\u0dba \u0dba\u0db1\u0dd4 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0dda \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0db6\u0dd2\u0db8\u0dca\u0db6 \u0dc3\u0dd2\u0dba\u0dbd\u0dca\u0dbd\u0daf \u0d85\u0da9\u0d82\u0d9c\u0dd4 \u0dc0\u0db1 \u0dc3\u0dda \u0d85\u0dbb\u0dca\u0dae \u0daf\u0d9a\u0dca\u0dc0\u0dcf \u0d9c\u0db1\u0dd4 \u0dbd\u0db6\u0db1 \u0d95\u0db1\u0dd1\u0db8 \u0d9a\u0dd4\u0dbd\u0d9a\u0dba\u0d9a\u0dd2.<\/li><li>\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a \u0d9a\u0dd4\u0da9\u0dcf\u0db8 \u0dc3\u0dc4\u0dc0\u0dc3\u0db8\u0dba \u0db4\u0dbb\u0dcf\u0dc3\u0dba \u0db1\u0db8\u0dca \u0dc0\u0dda.<\/li><li>x \u0d9a\u0dd4\u0dbd\u0d9a\u0dba\u0dda 1,2,3 &nbsp;\u0d85\u0dc0\u0dba\u0dc0 f \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0db8\u0d9c\u0dd2\u0db1\u0dca y \u0d9a\u0dd4\u0dbd\u0d9a\u0dba\u0dda \u0d87\u0dad\u0dd2 1,4,9 \u0d85\u0dc0\u0dba\u0dc0 \u0dc0\u0dbd\u0da7 \u0d85\u0db1\u0dd4\u0dbb\u0dd4\u0db4 \u0dc0\u0db1 \u0db1\u0dd2\u0dc3\u0dcf \u0d92\u0dc0\u0dcf x \u0d9a\u0dd4\u0dbd\u0d9a\u0dba\u0dda \u0d85\u0dc0\u0dba\u0dc0 \u0dc0\u0dbd\u0da7 \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0db6\u0dd2\u0db8\u0dca\u0db7 \u0dbd\u0dd9\u0dc3 \u0dc4\u0daf\u0dd4\u0db1\u0dca\u0dc0\u0dba\u0dd2. \u0db8\u0dd9\u0db8 \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0db6\u0dd2\u0db8\u0dca\u0db7 \u0dc0\u0dbd\u0dd2\u0db1\u0dca \u0dc3\u0db8\u0db1\u0dca\u0dc0\u0dd2\u0dad \u0d9a\u0dd4\u0dbd\u0d9a\u0dba {1,4,9 }&nbsp; \u201cf \u201c \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0dda \u0db4\u0dbb\u0dcf\u0dc3\u0dba ( Range) \u0dbd\u0dd9\u0dc3 \u0dc4\u0daf\u0dd4\u0db1\u0dca\u0dc0\u0db1\u0dd4 \u0dbd\u0db6\u0db1 \u0d85\u0dad\u0dbb \u0d91\u0dba&nbsp; \u201cR<sub>f <\/sub>\u201c \u0dbd\u0dd9\u0dc3 \u0dc3\u0d82\u0d9a\u0dda\u0dad \u0d9a\u0dbb\u0dba\u0dd2.<\/li><li>\u0db8\u0dd9\u0dc4\u0dd2&nbsp; D<sub>f&nbsp; <\/sub>= {1 ,2 ,3} \u0daf R<sub>f&nbsp; <\/sub>= {1,4,9} \u0daf C<sub>f <\/sub>&nbsp;= {1,2,3,4,5,6,7,8,9} \u0daf \u0dc0\u0dda.<\/li><\/ul>\n\n\n\n<p><strong>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab<\/strong>:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}y=3x+2\\;\\text{\u0dc4\u0dcf\u00a0}D_f=\\{\\;x\\in\\mathbb{R}\/0&lt;x&lt;5\\;\\}\\;\\text{\u0db1\u0db8\u0dca\u00a0}y\\;\\text{\u0dc4\u0dd2\u00a0\u0db4\u0dbb\u0dcf\u0dc3\u0dba\u00a0\u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.}\\\\y=3x+2\\;;\\;x=\\frac{(y-2)}3\\end{array}<\/span><\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}0\\;&amp;&lt;&amp;\\;x\\;&amp;&lt;&amp;\\;5\\\\0\\;&amp;&lt;&amp;\\;\\frac{(y-2)}3\\;&amp;&lt;&amp;\\;5\\\\0\\;&amp;&lt;&amp;\\;y-2\\;&amp;&lt;&amp;\\;15\\\\2\\:&amp;&lt;&amp;\\;y\\;&amp;&lt;&amp;\\;17\\;\\end{array}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">R_f\\in\\left(2,17\\right)<\/span><\/p>\n\n\n\n<ol class=\"wp-block-list\"><li><span class=\"wp-katex-eq\" data-display=\"false\">f(x)=x^2+1\\;\\text{\u0dc4\u0dcf\u00a0}D_f=\\{\\;x\\in R\/-3&lt;x&lt;+3\\;\\}\\;\\text{\u0db1\u0db8\u0dca\u00a0}f(x)\\;\\text{\u0dc4\u0dd2\u00a0\u0db4\u0dbb\u0dcf\u0dc3\u0dba\u00a0\u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.}<\/span><\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}-3\\;&amp;&lt;&amp;\\;\\;\\;\\;\\;x\\;&amp;&lt;&amp;\\;+3\\\\0\\;&amp;&lt;&amp;\\;\\;\\;\\;\\;x^2\\;&amp;&lt;&amp;\\;5\\\\1\\;&amp;&lt;&amp;\\;x^2+1\\;&amp;&lt;&amp;\\;15\\\\1\\:&amp;&lt;&amp;\\;\\;\\;f(x)&amp;&lt;&amp;\\;17\\;\\end{array}<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">R_f\\in\\left(1,10\\right)<\/span><\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span style=\"color:#304170\" class=\"has-inline-color\"><strong>\u0db8\u0dad\u0da7 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad<\/strong><\/span><\/h4>\n\n\n\n<ul class=\"wp-block-list\"><li>f \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0dda \u0db4\u0dbb\u0dcf\u0dc3\u0dba \u0dc4\u0dcf \u0dc3\u0dc4-\u0dc0\u0dc3\u0db8 \u0dc3\u0db8\u0dcf\u0db1 \u0dc0\u0dda \u0db1\u0db8\u0dca,&nbsp; f \u0dba\u0db1\u0dd4 \u0db8\u0dad\u0da7 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0dc0\u0dda.<\/li><\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><span style=\"color:#304170\" class=\"has-inline-color\"><strong>\u0d91\u0d9a\u0da7 \u0d91\u0d9a \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad<\/strong><\/span><\/h4>\n\n\n\n<ul class=\"wp-block-list\"><li>\u0dc0\u0dc3\u0db8\u0dba\u0dda x<sub>1 <\/sub>&nbsp;\u0dc4\u0dcf x<sub>2 <\/sub>&nbsp;\u0d85\u0d9c\u0dba\u0db1\u0dca \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0dc3\u0daf\u0dc4\u0dcf f (x<sub>1<\/sub>) = f (x<sub>2<\/sub>) \u0db1\u0db8\u0dca x<sub>1 <\/sub>= x<sub>2<\/sub> \u0dc0\u0db1 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0d91\u0d9a\u0da7 \u0d91\u0d9a \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0dc0\u0dda.<\/li><\/ul>\n\n\n\n<p>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab:<\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">y=\\sqrt{3x+1}\\;\\text{\u0d91\u0d9a\u0da7\u00a0\u0d91\u0d9a\u00a0\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca\u00a0\u0db6\u0dc0\u00a0\u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.}<\/span>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}f\\left(x_1\\right)\\;&amp;=&amp;\\;f\\left(x_2\\right)\\\\\\sqrt{3x_1+1}\\;&amp;=&amp;\\;\\sqrt{3x_2+1}\\\\3x_1+1\\;&amp;=&amp;\\;3x_2+1\\\\3x_1\\;&amp;=&amp;\\;3x_2\\\\x_1\\;&amp;=&amp;\\;x_2\\end{array}<\/span><\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span style=\"color:#304170\" class=\"has-inline-color\">\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dd2\u0dba \u0d85\u0d82\u0d9a\u0db1\u0dba<\/span><\/h4>\n\n\n\n<ul class=\"wp-block-list\"><li>f \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0dba\u0da7\u0dad\u0dda x \u0d9a\u0dd4\u0dbd\u0d9a\u0dba , y \u0d9a\u0dd4\u0dbd\u0d9a\u0dba\u0da7 \u0d85\u0db1\u0dd4\u0dbb\u0dd4\u0db4\u0dc0\u0dda \u0db1\u0db8\u0dca \u0d91\u0dba \u0dc3\u0d82\u0d9a\u0dda\u0dad\u0dcf\u0dad\u0dca\u0db8\u0d9a\u0dc0,<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\">&#8221; <span class=\"wp-katex-eq\" data-display=\"false\">f:x\\rightarrow y<\/span>&#8221;&nbsp;\u0dbd\u0dd9\u0dc3 \u0daf\u0d9a\u0dca\u0dc0\u0dba\u0dd2.<\/p>\n\n\n\n<p class=\"has-text-align-center\">x \u2208 X \u0dc4\u0dcf&nbsp;y \u2208 Y&nbsp;\u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>f \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0dda X \u0d9a\u0dd4\u0dbd\u0d9a\u0dba\u0dda x \u0d85\u0dc0\u0dba\u0dc0\u0dba \u0dc4\u0dcf Y \u0d9a\u0dd4\u0dbd\u0d9a\u0dba\u0dda y&nbsp; \u0d85\u0dc0\u0dba\u0dc0\u0dba \u0d85\u0db1\u0dd4\u0db4\u0dbb\u0dd4\u0db4 \u0dc0\u0dda \u0db1\u0db8\u0dca \u0d91\u0dba\u0daf <span class=\"wp-katex-eq\" data-display=\"false\">f:x\\rightarrow y<\/span> \u0dbd\u0dd9\u0dc3 \u0daf\u0d9a\u0dca\u0dc0\u0db1\u0dd4 \u0dbd\u0db6\u0db1 \u0d85\u0dad\u0dbb y \u0dba\u0db1\u0dd4 f \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0dba\u0da7\u0dad\u0dda x \u0dc4\u0dd2 \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0db6\u0dd2\u0db8\u0dca\u0db7\u0dba \u0dbd\u0dd9\u0dc3 \u0dc4\u0daf\u0dd4\u0db1\u0dca\u0dc0\u0db1 \u0d85\u0dad\u0dbb \u0d91\u0dba f (x ) \u0dbd\u0dd9\u0dc3 \u0dc3\u0d82\u0d9a\u0dda\u0dad \u0d9a\u0dbb\u0dba\u0dd2.<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\">&nbsp;&nbsp;x \u2208 X&nbsp;&nbsp;\u0dc4\u0dcf&nbsp;&nbsp;y \u2208 Y  \u0dc0\u0dd2\u0da7<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">f:x\\rightarrow y<\/span><\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">f:x\\rightarrow f(x)\\;\\;<\/span>\u0dc0\u0dda.&nbsp;&nbsp; \u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf<span class=\"wp-katex-eq\" data-display=\"false\">\\;\\;y=f\\left(x\\right)\\;\\;<\/span> \u0dc0\u0dda.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span style=\"color:#304170\" class=\"has-inline-color\">\u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba\u0dba<\/span><\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>\u0db1\u0dd2\u0dbb\u0dad\u0dd4\u0dbb\u0dd4\u0dc0\u0db8 \u0dc0\u0dd9\u0db1\u0dc3\u0dca \u0dc0\u0db1 \u0d85\u0d9c\u0dba\u0db1\u0dca \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba\u0dba \u0dbd\u0dd9\u0dc3 \u0dc4\u0daf\u0dd4\u0db1\u0dca\u0dc0\u0dba\u0dd2.<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><span style=\"color:#304170\" class=\"has-inline-color\">\u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba\u0dba \u0dc4\u0dcf \u0db4\u0dbb\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba\u0dba<\/span><\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>X&nbsp; \u0d9a\u0dd4\u0dbd\u0d9a\u0dba\u0dda&nbsp; x \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba \u0dc0\u0dd9\u0db1\u0dc3\u0dca \u0dc0\u0db1 \u0db1\u0dd2\u0dc3\u0dcf \u0d91\u0dba <strong>\u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0dad\u0dca\u0dad \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba\u0dba<\/strong> \u0dbd\u0dd9\u0dc3 \u0dc4\u0daf\u0dd4\u0db1\u0dca\u0dc0\u0dba\u0dd2.<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-list\"><li>x \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0da7 \u0d85\u0db1\u0dd4\u0dbb\u0dd4\u0db4 \u0dc0\u0db1 \u0db1\u0dd2\u0dc3\u0dcf y \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba <strong>\u0db4\u0dbb\u0dcf\u0dba\u0dad\u0dca\u0dad <strong>\u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba\u0dba<\/strong><\/strong> \u0dbd\u0dd9\u0dc3\u0dad\u0dca \u0dc4\u0daf\u0dd4\u0db1\u0dca\u0dc0\u0dba\u0dd2.<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"has-inline-color has-black-color\">\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0d9a\u0dbb\u0dca\u0db8<\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><strong><span style=\"color:#304170\" class=\"has-inline-color\">\u0db1\u0dd2\u0dba\u0dad\u0dba\u0d9a \u0dc4\u0dcf \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a \u0d9c\u0dd4\u0dab\u0dd2\u0dad\u0dba \u0dc3\u0daf\u0dc4\u0dcf \u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd3\u0db8.<\/span><\/strong><\/h3>\n\n\n\n<p>&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">f:x\\rightarrow f(x)<\/span> \u0dc0\u0db1 \u0db4\u0dbb\u0dd2\u0daf\u0dd2 \u201c f \u201c&nbsp; \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0d85\u0dbb\u0dca\u0dae \u0daf\u0d9a\u0dca\u0dc0\u0dcf \u0d87\u0dad\u0dd2 \u0dc0\u0dd2\u0da7 K&nbsp; \u0db1\u0dd2\u0dba\u0dad\u0dba\u0dda \u0dc4\u0dcf f \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0dda \u0d9c\u0dd4\u0dab\u0dd2\u0dad\u0dba&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center\">(K) f(x) = Kf(x)&nbsp;; x \u2208 R \u0dbd\u0dd9\u0dc3 \u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dda.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong><span style=\"color:#304170\" class=\"has-inline-color\">\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0daf\u0dd9\u0d9a\u0d9a \u0d93\u0d9a\u0dca\u200d\u0dba<\/span><\/strong><\/h3>\n\n\n\n<p class=\"has-text-align-center\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <span class=\"wp-katex-eq\" data-display=\"false\">f:x\\rightarrow f(x)\\;\\text{\u0dba\u0dba\u0dd2\u0daf}\\;g:x\\rightarrow g(x)\\;\\text{\u0dba\u0dba\u0dd2\u0daf\u00a0\u0d9c\u0db1\u0dd2\u0db8\u0dd4.}<\/span><\/p>\n\n\n\n<p>f \u0dc4\u0dcf g \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0daf\u0dd9\u0d9a\u0dd9\u0dc4\u0dd2 \u0d93\u0d9a\u0dca\u200d\u0dba ( f + g ) \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0daf\u0d9a\u0dca\u0dc0\u0db1 \u0d85\u0dad\u0dbb,<\/p>\n\n\n\n<p class=\"has-text-align-center\">(f+g)x = f(x)+g(x)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u0dbd\u0dd9\u0dc3 \u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dda.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong><span style=\"color:#304170\" class=\"has-inline-color\">\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0daf\u0dd9\u0d9a\u0d9a <strong>\u0d85\u0db1\u0dca\u0dad\u0dbb\u0dba<\/strong><\/span><\/strong><\/h3>\n\n\n\n<p>f \u0dc4\u0dcf g \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0daf \u0d91\u0d9a\u0dd9\u0dc4\u0dd2 \u0d85\u0db1\u0dca\u0dad\u0dbb\u0dba ( f \u2013 g ) \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0daf\u0d9a\u0dca\u0dc0\u0db1 \u0d85\u0dad\u0dbb,<\/p>\n\n\n\n<p class=\"has-text-align-center\">(f-g)x = f(x)-g(x)&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;\u0dbd\u0dd9\u0dc3 \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dda.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong><span style=\"color:#304170\" class=\"has-inline-color\">\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0daf\u0dd9\u0d9a\u0d9a <strong><strong>\u0d9c\u0dd4\u0dab\u0dd2\u0dad\u0dba<\/strong><\/strong><\/span><\/strong><\/h3>\n\n\n\n<p>f \u0dc4\u0dcf g \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0daf\u0dd9\u0d9a\u0dd9\u0dc4\u0dd2 \u0d9c\u0dd4\u0dab\u0dd2\u0dad\u0dba fg \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0daf\u0d9a\u0dca\u0dc0\u0db1 \u0d85\u0dad\u0dbb,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\boldsymbol(\\boldsymbol f\\boldsymbol g\\boldsymbol)\\boldsymbol x&amp;\\boldsymbol=&amp;\\boldsymbol f\\boldsymbol(\\boldsymbol x\\boldsymbol)\\boldsymbol\\times\\boldsymbol g\\boldsymbol(\\boldsymbol x\\boldsymbol)\\end{array}<\/span>&nbsp;&nbsp;&nbsp; \u0dbd\u0dd9\u0dc3 \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dda.&nbsp;&nbsp; <\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong><span style=\"color:#304170\" class=\"has-inline-color\">\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0daf\u0dd9\u0d9a\u0d9a <strong><strong><strong>\u0d85\u0db1\u0dd4\u0db4\u0dcf\u0dad\u0dba<\/strong><\/strong><\/strong><\/span><\/strong><\/h3>\n\n\n\n<p>f \u0dc4\u0dcf g \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0daf\u0dd9\u0d9a\u0dd9\u0dc4\u0dd2 \u0d85\u0db1\u0dd4\u0db4\u0dcf\u0dad\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">\\frac fg<\/span>&nbsp; \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0daf\u0d9a\u0dca\u0dc0\u0db1 \u0d85\u0dad\u0dbb&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\left(\\frac{\\mathbf f}{\\mathbf g}\\right)\\boldsymbol x&amp;\\boldsymbol=&amp;\\frac{\\mathbf f\\left(\\mathbf x\\right)}{\\mathbf g\\left(\\mathbf x\\right)}\\end{array}<\/span>&nbsp;&nbsp;&nbsp; \u0dc3\u0dc4 g(x)\u2260 0 \u0dbd\u0dd9\u0dc3 \u0d85\u0dbb\u0dca\u0dae \u0daf\u0d9a\u0dca\u0dc0\u0dba\u0dd2.<\/p>\n\n\n\n<div class=\"wp-block-cover alignfull has-background-dim\" style=\"background-color:#f5e8c7\"><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#6f4c5b;font-size:20px\">\u0db4\u0dc4\u0dad \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dba\u0dd9\u0db1\u0dca \u0db4\u0dc4\u0dc3\u0dd4\u0dc0\u0dd9\u0db1\u0dca \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8\u0da7 \u0d8b\u0dad\u0dca\u0dc3\u0dcf\u0dc4 \u0d9a\u0dbb\u0db8\u0dd4.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color\" style=\"color:#6f4c5b;font-size:30px\"><span class=\"wp-katex-eq\" data-display=\"false\">2\\sqrt[3]{2x+1}=x^3-1<\/span><\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link has-text-color has-background\" href=\"https:\/\/learnsteer.sasnaka.org\/science\/alscience\/02-02-00-q1\/\" style=\"border-radius:10px;background:linear-gradient(135deg,rgb(158,119,119) 0%,rgb(158,119,119) 100%);color:#f3e4be\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1<\/a><\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"has-inline-color has-black-color\">\u0dc0\u0dd2\u0dc0\u0dd2\u0db0 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad<\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><strong><span style=\"color:#304170\" class=\"has-inline-color\"><strong>\u0db1\u0dd2\u0dba\u0dad \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad<\/strong><\/span><\/strong><\/h3>\n\n\n\n<p>\u0dc3\u0dd2\u0dba\u0dbd\u0dd4 x \u2208 R \u0dc3\u0daf\u0dc4\u0dcf f(x) = K ; {K \u0db1\u0dd2\u0dba\u0dad\u0dba\u0d9a\u0dd2}&nbsp; \u0dbd\u0dd9\u0dc3 \u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 x \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0db1\u0dd2\u0dba\u0dad&nbsp;\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0dca \u0dbd\u0dd9\u0dc3 \u0dc4\u0daf\u0dd4\u0db1\u0dca\u0dc0\u0dba\u0dd2.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong><span style=\"color:#304170\" class=\"has-inline-color\"><strong><strong>\u0d92\u0d9a\u0d9a<\/strong> \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad<\/strong><\/span><\/strong><\/h3>\n\n\n\n<p>x \u2208 R \u0dc3\u0daf\u0dc4\u0dcf f(x) = 1 \u0dc0\u0db1 \u0db4\u0dbb\u0dd2\u0daf\u0dd2 \u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0d92\u0d9a\u0d9a \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0dbd\u0dd9\u0dc3 \u0dc4\u0daf\u0dd4\u0db1\u0dca\u0dc0\u0dba\u0dd2<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong><span style=\"color:#304170\" class=\"has-inline-color\"><strong><strong>\u0d89\u0dbb\u0da7\u0dca\u0da7\u0dda<\/strong> \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad<\/strong><\/span><\/strong><\/h3>\n\n\n\n<p>x \u2208 R \u0dc3\u0daf\u0dc4\u0dcf f(-x) = f(x) \u0dc0\u0db1 \u0db4\u0dbb\u0dd2\u0daf\u0dd2 \u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0d89\u0dbb\u0da7\u0dca\u0da7\u0dda \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0dbd\u0dd9\u0dc3 \u0dc4\u0daf\u0dd4\u0db1\u0dca\u0dc0\u0dba\u0dd2<\/p>\n\n\n\n<p>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab: f(x) = 4 \u2013 x<sup>2<\/sup>&nbsp; \u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; f  \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0d89\u0dbb\u0da7\u0dca\u0da7\u0dda \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0dba\u0dd0\u0dba\u0dd2 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1. <span class=\"wp-katex-eq\" data-display=\"false\">-3\\leq x\\leq3<\/span> \u0db4\u0dca\u200d\u0dbb\u0dcf\u0db1\u0dca\u0dad\u0dbb\u0dba \u0dad\u0dd4\u0dbd y = f(x) \u0dc4\u0dd2 \u0d85\u0d9c\u0dba\u0db1\u0dca \u0dbd\u0dd2\u0dba\u0dcf \u0daf\u0d9a\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}f\\left(x\\right)\\;&amp;=&amp;\\;4-x^2\\\\\\text{\u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf}\\;f\\left(-x\\right)\\;&amp;=&amp;\\;4-\\;(-x)^2\\\\&amp;=&amp;\\;4-\\;x^2\\\\&amp;=&amp;\\;f(x)\\;\\end{array}<\/span>\n\n\n\n<p>\u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf \u0db8\u0dd9\u0dba \u0d89\u0dbb\u0da7\u0dca\u0da7\u0dda \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dd2.<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">x<\/td><td class=\"has-text-align-center\" data-align=\"center\">&nbsp;-3<\/td><td class=\"has-text-align-center\" data-align=\"center\">-2<\/td><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">y = f(x) = 4-x<sup>2<\/sup><\/td><td class=\"has-text-align-center\" data-align=\"center\">&nbsp; -5<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">-5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong><span style=\"color:#304170\" class=\"has-inline-color\"><strong><strong>\u0d94\u0dad\u0dca\u0dad\u0dda<\/strong> \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad<\/strong><\/span><\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>x \u2208R \u0dc3\u0daf\u0dc4\u0dcf f(-x) = -f(x) \u0dc0\u0db1 \u0db4\u0dbb\u0dd2\u0daf\u0dd2 \u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0d94\u0dad\u0dca\u0dad\u0dda \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0dbd\u0dd9\u0dc3 \u0dc4\u0daf\u0dd4\u0db1\u0dca\u0dc0\u0dba\u0dd2.\u0d94\u0dad\u0dca\u0dad\u0dda \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a \u0daf\u0dbd \u0dc3\u0da7\u0dc4\u0db1 \u0db8\u0dd4\u0dbd \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba \u0dc0\u0da7 \u0dc3\u0db8\u0db8\u0dd2\u0dad\u0dd2\u0d9a \u0dc0\u0dda.<\/li><\/ul>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab :&nbsp; f(x) = x<sup>5 <\/sup>\u2013 x<sup>3 <\/sup>+ x&nbsp; \u0dc3\u0dbd\u0d9a\u0db8\u0dd4.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}f(-x)&amp;=&amp;(-x)^5-(-x)^3+(-x)\\\\&amp;=&amp;-\\{x^5-x^3+x\\}\\\\&amp;=&amp;-f(x)\\end{array}<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf f \u0dba\u0db1\u0dd4 \u0d94\u0dad\u0dca\u0dad\u0dda \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dd2.<\/li><li>f(x) = x<sup>3<\/sup> \u0dc3\u0dbd\u0d9a\u0db8\u0dd4.<\/li><li><span class=\"wp-katex-eq\" data-display=\"false\">-2\\;\\leq x\\;\\;\\leq2\\;\\text{\u0db4\u0dbb\u0dcf\u0dc3\u0dba\u00a0\u0dad\u0dd4\u0dbd}\\;y\\;=\\;f(x)\\;\\text{\u0dc4\u0dd2\u00a0\u0d85\u0d9c\u0dba\u0db1\u0dca\u00a0\u0dbd\u0dd2\u0dba\u0dcf\u00a0\u0daf\u0d9a\u0dca\u0dc0\u0db1\u0dca\u0db1}.<\/span><\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}f(-x)\\;&amp;=&amp;\\;(-x)^3\\&amp;=&amp;\\;-\\;x^3\\&amp;=&amp;\\;-\\;f(x)\\end{array}<\/span><\/p>\n\n\n\n<p>\u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf \u0db8\u0dd9\u0dba \u0d94\u0dad\u0dca\u0dad\u0dda \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dd2.<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">x<\/td><td class=\"has-text-align-center\" data-align=\"center\">-2<\/td><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">y=f(x)<\/td><td class=\"has-text-align-center\" data-align=\"center\">-8<\/td><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">8<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong><span style=\"color:#304170\" class=\"has-inline-color\"><strong><strong><strong>\u0dc3\u0d82\u0dba\u0dd4\u0dad<\/strong><\/strong><\/strong><\/span><\/strong> <strong><span style=\"color:#304170\" class=\"has-inline-color\"><strong>\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad<\/strong><\/span><\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>f \u0dba\u0db1\u0dd4 g \u0dc4\u0dd2 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0daf g \u0dba\u0db1\u0dd4 x \u0dc4\u0dd2 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0daf \u0db1\u0db8\u0dca f \u0dba\u0db1\u0dd4 x \u0dc4\u0dd2 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0dc0\u0dda.\u0d91\u0dba fog(x) = f[g(x)] \u0dbd\u0dd9\u0dc3 \u0db1\u0db8\u0dca \u0dc0\u0dda.<\/li><\/ul>\n\n\n\n<p>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab:<\/p>\n\n\n\n<p>f(x) = x \u2013 3 \u0daf gof(x) = x<sup>2 <\/sup>\u2013 6x + 11 \u0daf \u0db1\u0db8\u0dca g(x) \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1. fog(x) \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}gof(x)\\;&amp;=&amp;\\;x^2\\;\u2013\\;6x\\;+\\;11\\\\g\\left[f\\left(x\\right)\\right]&amp;=&amp;\\;(x\\;-3)2\\;+\\;2\\\\&amp;=&amp;\\;\\left[f\\left(x\\right)\\right]^2\\;+\\;2\\\\g\\left(x\\right)\\;&amp;=&amp;\\;x^2\\;+\\;2\\\\\\\\{fog(x)\\;}&amp;=&amp;\\;f\\left[g\\left(x\\right)\\right]\\\\&amp;=&amp;{\\;g\\left(x\\right)\\;-\\;3}\\\\&amp;=&amp;\\;x^2\\;+\\;2\\;-\\;3\\\\&amp;=&amp;\\;x^2\\;-\\;1\\end{array}<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong><span style=\"color:#304170\" class=\"has-inline-color\"><strong><strong><strong>\u0d9a\u0da9\u0db8\u0db1\u0dd2\u0db1\u0dca&nbsp;<\/strong><\/strong>\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad<\/strong><\/span><\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>\u0dc0\u0dc3\u0db8\u0dba\u0dda \u0dc0\u0dd2\u0dc0\u0dd2\u0db0 \u0db4\u0dca\u200d\u0dbb\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0dc0\u0dbd\u0daf\u0dd3 \u0dc0\u0dd2\u0dc0\u0dd2\u0db0 \u0dbd\u0dd9\u0dc3 \u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0dc0\u0dda.<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}f\\left(x\\right)\\;\\rightarrow\\;2x\\;+\\;3\\;\\;\\;;\\;\\;\\;x\\;\\geq\\;1\\\\\\;\\;\\;\\;\\;\\;\\;\\;\\rightarrow\\;x^2\\;\\;\\;;\\;\\;\\;x\\;&lt;\\;1\\end{array}<\/span><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"358\" height=\"237\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/06\/image-123.png\" alt=\"\" class=\"wp-image-17530\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/06\/image-123.png 358w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/06\/image-123-300x199.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/06\/image-123-150x99.png 150w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/06\/image-123-356x237.png 356w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-white-color has-text-color has-background\" style=\"background-color:#272062\"><p class=\"has-white-color has-text-color has-background\" style=\"background-color: #272062;text-align: center\"><strong><span style=\"font-family: 'book antiqua', palatino, serif\"><em><span style=\"font-size: 18pt;color: #ffffff\">&#8220;Politics is for the present, but an equation is for eternity.&#8221;<\/span><\/em><\/span><\/strong><br><span style=\"font-size: 10pt;color: #bdbaa2;font-family: tahoma, arial, helvetica, sans-serif\">-Albert Einstein &#8211;<\/span><\/p><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Video Links :<\/h4>\n\n\n<div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_82824\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/52tpYl2tTqk?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=0&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;\" class=\"__youtube_prefs__  no-lazyload\" title=\"YouTube player\"  allow=\"fullscreen; accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen data-no-lazy=\"1\" data-skipgform_ajax_framebjll=\"\"><\/iframe><\/div>\n\n<div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_75111\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/3gaxVHVI4cI?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=0&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;\" class=\"__youtube_prefs__  no-lazyload\" title=\"YouTube player\"  allow=\"fullscreen; accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen data-no-lazy=\"1\" data-skipgform_ajax_framebjll=\"\"><\/iframe><\/div>\n\n<div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_41258\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/djT6-YamHaA?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=0&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;\" 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