{"id":9815,"date":"2022-01-28T01:49:42","date_gmt":"2022-01-27T20:19:42","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9815"},"modified":"2022-01-28T01:49:43","modified_gmt":"2022-01-27T20:19:43","slug":"many-one-function-definition-and-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/many-one-function-definition-and-examples\/","title":{"rendered":"Many One Function – Definition and Examples"},"content":{"rendered":"

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

Let’s begin –<\/p>\n

Many One Function<\/h2>\n

Definition<\/strong> : A function f : A \\(\\rightarrow\\) B is said to be a many-one function if two or more elements of set A have the same image in B.<\/p>\n

Thus, f : A \\(\\rightarrow\\) B is a many-one if there exist x, y \\(\\in\\) A such that x \\(\\ne\\) y but f(x) = f(y).<\/p><\/blockquote>\n

In other words, f : A \\(\\rightarrow\\) B is a many-one if it is not a one-one function.<\/p>\n

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

Example<\/strong><\/span> : Let f : A \\(\\rightarrow\\) B and g : X \\(\\rightarrow\\) Y be two functions represented by the following diagrams :<\/p>\n

\"many\"many<\/p>\n

Solution<\/strong><\/span> : Clearly, a2 \\(\\ne\\) a4 but f(a2) = f(a4) and x1 \\(\\ne\\) x2 but g(x1) = g(x2). So, f and g are many-one.<\/p>\n

Example<\/strong><\/span> : Let A = {-1, 1, -2, 2} and B = {1, 4, 9, 16}. Consider f : A \\(\\rightarrow\\) B given by f(x) = \\(x^2\\).<\/p>\n

Solution<\/strong><\/span> : Then, f(-1) = 1, f(1) = 1, f(-2) = 4 and f(2) = 4. Thus, 1 and -1 have the same image. Similarly, 2 and -2 also have the same image. So, f is many-one.<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is many one function with definition and examples. Let’s begin – Many One Function Definition : A function f : A \\(\\rightarrow\\) B is said to be a many-one function if two or more elements of set A have the same image in B. Thus, f : A \\(\\rightarrow\\) B …<\/p>\n

Many One 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":[359,368,834],"yoast_head":"\nMany One Function - Definition and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is many one 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\/many-one-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=\"Many One Function - 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