{"id":4259,"date":"2022-06-10T19:05:16","date_gmt":"2022-06-10T19:05:16","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4259"},"modified":"2022-06-10T19:05:16","modified_gmt":"2022-06-10T19:05:16","slug":"inverse-of-a-rational-function","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/10\/inverse-of-a-rational-function\/","title":{"rendered":"Inverse of a Rational Function"},"content":{"rendered":"\n<p>To find the\u00a0inverse\u00a0of a rational function y = f(x):<\/p>\n\n\n\n<ul><li>Replace f(x) with y.<\/li><li>Interchange x and y.<\/li><li>Solve the resultant equation for y.<\/li><li>The result would give the inverse f<sup>-1<\/sup>(x).<\/li><\/ul>\n\n\n\n<p><strong>Example:<\/strong>&nbsp;Find the inverse of the rational function f(x) = (2x &#8211; 1) \/ (x + 3).<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>The given function can be written as:<\/p>\n\n\n\n<p>y = (2x &#8211; 1) \/ (x + 3)<\/p>\n\n\n\n<p>Interchanging x and y:<\/p>\n\n\n\n<p>x = (2y &#8211; 1) \/ (y + 3)<\/p>\n\n\n\n<p>Now, we will solve for y.<\/p>\n\n\n\n<p>x(y + 3) = 2y &#8211; 1<\/p>\n\n\n\n<p>xy + 3x = 2y &#8211; 1<\/p>\n\n\n\n<p>3x + 1 = 2y &#8211; xy<\/p>\n\n\n\n<p>3x + 1 = y (2 &#8211; x)<\/p>\n\n\n\n<p>y = (3x + 1) \/ (2 &#8211; x) = f<sup>-1<\/sup>(x)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>To find the\u00a0inverse\u00a0of a rational function y = f(x): Replace f(x) with y. Interchange x and y. Solve the resultant equation for y. The result would give the inverse f-1(x). Example:&nbsp;Find the inverse of the rational function f(x) = (2x &#8211; 1) \/ (x + 3). Solution: The given function can be written as: y [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[715],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4259"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=4259"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4259\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4259"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4259"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}