{"id":9845,"date":"2022-01-28T02:00:43","date_gmt":"2022-01-27T20:30:43","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9845"},"modified":"2022-01-28T02:00:47","modified_gmt":"2022-01-27T20:30:47","slug":"what-is-composition-of-functions","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-composition-of-functions\/","title":{"rendered":"What is Composition of Functions ?"},"content":{"rendered":"

Here you will learn what is composition of functions with properties and examples.<\/p>\n

Let’s begin –<\/p>\n

What is Composition of Functions ?<\/h2>\n

Let f : A \\(\\rightarrow\\) B & g : f : B \\(\\rightarrow\\) C be two functions. Then the function gof : f : A \\(\\rightarrow\\) C defined by (gof)(x) = g(f(x)) \\(\\forall\\) x \\(\\in\\) A is called the composite of the two function f & g.<\/p>\n

Also Read<\/strong> : Types of Functions in Maths \u2013 Domain and Range<\/a><\/p>\n

Properties :<\/h2>\n

(a) In general composite of functions is not commutative i.e. gof \\(\\ne\\) fog.<\/p>\n

(b) The composition of functions is associative i.e. if f, g, h are three functions such that fo(goh) & (fog)oh are defined, then fo(goh) = (fog)oh.<\/p>\n

(c) The composition of two bijections is a bijection i.e. if f & g are two bijections such that gof is defined, then gof is also a bijection.<\/p><\/blockquote>\n

Example<\/strong><\/span> : If f(x) = \\(x^2\\) + 1, g(x) = \\(1\\over x-1\\), then find (fog)(x).<\/p>\n

Solution<\/span><\/strong> : Now (fog)(x) = f(g(x)) = f(\\(1\\over x-1\\)) = f(z), where z = \\(1\\over x-1\\)<\/p>\n

= \\(z^2 + 1\\) [ \\(\\because\\) f(x) = \\(x^2 + 1\\) ]<\/p>\n

= \\(({1\\over x-1})^2\\) + 1 = \\(1\\over {(x-1)^2}\\) + 1<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is composition of functions with properties and examples. Let’s begin – What is Composition of Functions ? Let f : A \\(\\rightarrow\\) B & g : f : B \\(\\rightarrow\\) C be two functions. Then the function gof : f : A \\(\\rightarrow\\) C defined by (gof)(x) = g(f(x)) \\(\\forall\\) …<\/p>\n

What is Composition of Functions ?<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[26],"tags":[365,359],"yoast_head":"\nWhat is Composition of Functions ? - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is composition of functions with properties and examples based on it.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/what-is-composition-of-functions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is Composition of Functions ? - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"In this post you will learn what is composition of functions with properties and examples based on it.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/what-is-composition-of-functions\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-01-27T20:30:43+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-01-27T20:30:47+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/what-is-composition-of-functions\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/what-is-composition-of-functions\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"What is Composition of Functions ?\",\"datePublished\":\"2022-01-27T20:30:43+00:00\",\"dateModified\":\"2022-01-27T20:30:47+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/what-is-composition-of-functions\/\"},\"wordCount\":192,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"keywords\":[\"composite functions\",\"function\"],\"articleSection\":[\"Function\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/what-is-composition-of-functions\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/what-is-composition-of-functions\/\",\"url\":\"https:\/\/mathemerize.com\/what-is-composition-of-functions\/\",\"name\":\"What is Composition of Functions ? - Mathemerize\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2022-01-27T20:30:43+00:00\",\"dateModified\":\"2022-01-27T20:30:47+00:00\",\"description\":\"In this post you will learn what is composition of functions with properties and examples based on it.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/what-is-composition-of-functions\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/what-is-composition-of-functions\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/what-is-composition-of-functions\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"What is Composition of Functions ?\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"What is Composition of Functions ? - Mathemerize","description":"In this post you will learn what is composition of functions with properties and examples based on it.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/what-is-composition-of-functions\/","og_locale":"en_US","og_type":"article","og_title":"What is Composition of Functions ? - Mathemerize","og_description":"In this post you will learn what is composition of functions with properties and examples based on it.","og_url":"https:\/\/mathemerize.com\/what-is-composition-of-functions\/","og_site_name":"Mathemerize","article_published_time":"2022-01-27T20:30:43+00:00","article_modified_time":"2022-01-27T20:30:47+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/what-is-composition-of-functions\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/what-is-composition-of-functions\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"What is Composition of Functions ?","datePublished":"2022-01-27T20:30:43+00:00","dateModified":"2022-01-27T20:30:47+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/what-is-composition-of-functions\/"},"wordCount":192,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"keywords":["composite functions","function"],"articleSection":["Function"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/what-is-composition-of-functions\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/what-is-composition-of-functions\/","url":"https:\/\/mathemerize.com\/what-is-composition-of-functions\/","name":"What is Composition of Functions ? - Mathemerize","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2022-01-27T20:30:43+00:00","dateModified":"2022-01-27T20:30:47+00:00","description":"In this post you will learn what is composition of functions with properties and examples based on it.","breadcrumb":{"@id":"https:\/\/mathemerize.com\/what-is-composition-of-functions\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/what-is-composition-of-functions\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/what-is-composition-of-functions\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"What is Composition of Functions ?"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/9845"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=9845"}],"version-history":[{"count":2,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/9845\/revisions"}],"predecessor-version":[{"id":9847,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/9845\/revisions\/9847"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=9845"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=9845"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=9845"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}