{"id":197,"date":"2013-04-15T22:41:53","date_gmt":"2013-04-15T22:41:53","guid":{"rendered":"http:\/\/www.latinhire.com\/material\/?p=197"},"modified":"2014-06-28T08:15:19","modified_gmt":"2014-06-28T08:15:19","slug":"funciones-compuestas","status":"publish","type":"post","link":"https:\/\/www.latinhire.com\/es\/funciones-compuestas\/","title":{"rendered":"Funciones compuestas"},"content":{"rendered":"<p style=\"text-align: center;\"><a href=\"http:\/\/www.latinhire.com\/material\/wp-content\/uploads\/2013\/04\/juancruz.jpg\"><img decoding=\"async\" class=\"size-medium wp-image-198 aligncenter lazyload\" style=\"--smush-placeholder-width: 238px; --smush-placeholder-aspect-ratio: 238\/300;border: 1px solid black;\" title=\"juancruz\" data-src=\"http:\/\/www.latinhire.com\/material\/wp-content\/uploads\/2013\/04\/juancruz-238x300.jpg\" alt=\"\" width=\"238\" height=\"300\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" \/><\/a><\/p>\n<p><strong>Student<\/strong> I&#8217;m working on composite functions, but do not understand what the \u00abdomain\u00bb is or how to find it. I can work through the problem, but am lost when it comes to the domain. Please help!<\/p>\n<p><strong>(Tutor)<\/strong> Hi, my name is Juan. How are you today?<\/p>\n<p><strong>Student<\/strong> I&#8217;m well. How are you?<\/p>\n<p><strong>(Tutor)<\/strong> \u00a0I&#8217;m good :D, ok let&#8217;s get started!<\/p>\n<p><strong>Student<\/strong> ok. I&#8217;m needing to understand, what the \u00abdomain\u00bb is and how to find it?<\/p>\n<p><strong>(Tutor)<\/strong> \u00a0Sure!<\/p>\n<p>the domain is all the values that \u00abx\u00bb can take<br \/>\nfor example<br \/>\nlet&#8217;s find the domain of f(x)<br \/>\nf(x)=4x+1<br \/>\nin that case does x have any restriction?<br \/>\nI mean is there an x value that we can&#8217;t use?<\/p>\n<p><strong>Student<\/strong> no. I don&#8217;t think so<\/p>\n<p><strong>(Tutor)<\/strong> correct<br \/>\nso the domain of that function is all real numbers<br \/>\nfor example<br \/>\nthis function<br \/>\nis there an x value that we can&#8217;t use?<\/p>\n<p><strong>Student<\/strong> 0<\/p>\n<p><strong>(Tutor)<\/strong> You got it!<\/p>\n<p><strong>Student<\/strong> ok<\/p>\n<p><strong>(Tutor)<\/strong> \u00a0so the domain of this function is<br \/>\nall real numbers except zero<br \/>\nis it more clear?<br \/>\nor not?<br \/>\nshould I try to explain it in a different way?<\/p>\n<p><strong>Student<\/strong> yes.. domain is all values that x can be for the given function<\/p>\n<p><strong>(Tutor)<\/strong> \u00a0correct! \ud83d\ude00<\/p>\n<p><strong>Student<\/strong> ok<\/p>\n<p><strong>(Tutor)<\/strong> let&#8217;s go back to the problem<\/p>\n<p><strong>Student<\/strong> ok<\/p>\n<p><strong>(Tutor)<\/strong> \u00a0in this case<br \/>\nthe domain of f(x) is all real numbers<br \/>\nhow about g(x)?<\/p>\n<p><strong>Student<\/strong> I think i&#8217;m still slightly confused.<\/p>\n<p><strong>\u00a0(Tutor)<\/strong> in that function<br \/>\nis there any x value that we can&#8217;t use?<\/p>\n<p><strong>Student<\/strong> no, i don&#8217;t think so<\/p>\n<p><strong>(Tutor)<\/strong> Correct<\/p>\n<p><strong>Student<\/strong> ok<\/p>\n<p><strong>(Tutor)<\/strong> so the domain is all real numbers<\/p>\n<p><strong>Student<\/strong> yes<\/p>\n<p><strong>(Tutor)<\/strong> \u00a0Clue: the domain of a polynomial is always all real numbers<br \/>\nf(x) and g(x) are polynomials<\/p>\n<p><strong>Student<\/strong> ok. i see<\/p>\n<p><strong>(Tutor)<\/strong> so the domain will be all real numbers<br \/>\nand how about (fog)(x)<\/p>\n<p><strong>Student<\/strong> f(g(x))<\/p>\n<p><strong>(Tutor)<\/strong> correct \ud83d\ude00<br \/>\nbut they are asking for gof<\/p>\n<p><strong>Student<\/strong> yes<\/p>\n<p><strong>(Tutor)<\/strong> \u00a0ok do you know how to find it?<\/p>\n<p><strong>Student<\/strong> g(4x+1)<\/p>\n<p><strong>(Tutor)<\/strong> \u00a0yeah!<br \/>\nthen<br \/>\nwe have to use g<br \/>\nhow would it be?<br \/>\ndo you need help?<\/p>\n<p><strong>Student<\/strong> i think i&#8217;ve got it. I had trouble with the buttons<\/p>\n<p><strong>\u00a0(Tutor)<\/strong> \u00a0ohhh<br \/>\nwhat are you trying to do?<\/p>\n<p><strong>Student<\/strong> \u00a02(4x +1)squared + 5(4x+1)<\/p>\n<p><strong>(Tutor)<\/strong> \u00a0yeah!<\/p>\n<p><strong>Student<\/strong> \u00a02(16x <sup>2<\/sup> + 8x + 1) + 20x + 5<br \/>\n32x <sup>2<\/sup> + 16x + 2 + 20 + 5<\/p>\n<p><strong>(Tutor)<\/strong> \u00a0it is 20x<br \/>\nbut well done!<\/p>\n<p><strong>Student<\/strong> \u00a0equals 32x <sup>2<\/sup> + 36x +7<\/p>\n<p><strong>(Tutor)<\/strong> \u00a0\ud83d\ude00<br \/>\nYou got it!<br \/>\nAnd what&#8217;s the domain of that function?<br \/>\nI understand what you wrote<br \/>\nbut it should be written<br \/>\nlike&#8230;<\/p>\n<p><strong>Student<\/strong> \u00a0right, negative on the left<\/p>\n<p><strong>Student<\/strong>\u00a0Thank you so much for your help! \ud83d\ude42<\/p>\n<p><strong>(Tutor)<\/strong> \u00a0No problem! It was great to work with you!<br \/>\nBye<\/p>\n<p><strong>Student<\/strong> \u00a0thanks. Bye<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #000080;\">\u00a0<strong>Colaborador: Juan Cruz, Tutor Colombiano de \u00c1lgebra<\/strong><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Student I&#8217;m working on composite functions, but do not understand what the \u00abdomain\u00bb is or how to find it. I can work through the problem, but am lost when it comes to the domain. Please help! (Tutor) Hi, my name is Juan. How are you today? Student I&#8217;m well. How are you? (Tutor) \u00a0I&#8217;m good&hellip;<\/p>\n","protected":false},"author":9,"featured_media":3608,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"gallery","meta":{"footnotes":""},"categories":[81,89,88],"tags":[],"post_series":[],"class_list":["post-197","post","type-post","status-publish","format-gallery","has-post-thumbnail","hentry","category-algebra","category-ejemplos-de-tutorias","category-matematicas","post_format-post-format-gallery","entry","has-media"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.latinhire.com\/es\/wp-json\/wp\/v2\/posts\/197","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.latinhire.com\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.latinhire.com\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.latinhire.com\/es\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/www.latinhire.com\/es\/wp-json\/wp\/v2\/comments?post=197"}],"version-history":[{"count":1,"href":"https:\/\/www.latinhire.com\/es\/wp-json\/wp\/v2\/posts\/197\/revisions"}],"predecessor-version":[{"id":3609,"href":"https:\/\/www.latinhire.com\/es\/wp-json\/wp\/v2\/posts\/197\/revisions\/3609"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.latinhire.com\/es\/wp-json\/wp\/v2\/media\/3608"}],"wp:attachment":[{"href":"https:\/\/www.latinhire.com\/es\/wp-json\/wp\/v2\/media?parent=197"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.latinhire.com\/es\/wp-json\/wp\/v2\/categories?post=197"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.latinhire.com\/es\/wp-json\/wp\/v2\/tags?post=197"},{"taxonomy":"post_series","embeddable":true,"href":"https:\/\/www.latinhire.com\/es\/wp-json\/wp\/v2\/post_series?post=197"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}