{"id":9827,"date":"2022-01-28T01:50:09","date_gmt":"2022-01-27T20:20:09","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9827"},"modified":"2022-01-28T01:50:09","modified_gmt":"2022-01-27T20:20:09","slug":"into-function-definition-and-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/into-function-definition-and-examples\/","title":{"rendered":"Into Function – Definition and Examples"},"content":{"rendered":"

Here you will learn what is into function with definition and examples.<\/p>\n

Let’s begin –<\/p>\n

Into Function Definition<\/h2>\n

Definition<\/strong> : A function f : A \\(\\rightarrow\\) B is said to be an into function if every element of B having no pre-image in A.<\/p>\n

In other words, f : A \\(\\rightarrow\\) B is an into function if it is not an onto function.<\/p><\/blockquote>\n

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

Example<\/strong><\/span> : Let A \\(\\rightarrow\\) B be the function represented by the following diagram :<\/p>\n

\"into<\/p>\n

Solution<\/strong><\/span> : Clearly, b2 and b5 are two elements in B which do not have their pre-images in A. So, f : A \\(\\rightarrow\\) B is an into function.<\/p>\n

Example<\/strong><\/span> : A function f : N \\(\\rightarrow\\) N defined by f(x) = 2x is into function, because f(N) = {2, 4, 6, ….} \\(\\ne\\) N (co-domain). In other words, range (f) \\(\\ne\\) co-domain of f.<\/p>\n

Example<\/strong><\/span> : Let f : R \\(\\rightarrow\\) R given by f(x) = \\(x^2 + 2\\) for all x \\(\\in\\) R. Then, find whether it is into or not.<\/p>\n

Solution<\/strong><\/span> : Clearly, f(x) = \\(x^2 + 2\\) \\(\\ge\\) 2 for all x \\(\\in\\) R. So, negative real numbers in R (domain) do not have their pre-images in R (domain).<\/p>\n

Hence, f is an into function.<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is into function with definition and examples. Let’s begin – Into Function Definition Definition : A function f : A \\(\\rightarrow\\) B is said to be an into function if every element of B having no pre-image in A. In other words, f : A \\(\\rightarrow\\) B is an into …<\/p>\n

Into Function – Definition and Examples<\/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":[369,838,837],"yoast_head":"\nInto Function - Definition and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is into function with definition 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\/into-function-definition-and-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Into Function - 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