{"id":19839,"date":"2022-06-10T02:29:09","date_gmt":"2022-06-10T02:29:09","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4186"},"modified":"2022-06-10T02:29:09","modified_gmt":"2022-06-10T02:29:09","slug":"surjective-function","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/10\/surjective-function\/","title":{"rendered":"Surjective Function"},"content":{"rendered":"\n

A surjective function is defined between set A and set B, such that every element of set B is associated with at least one element of set A. The domain and range of a surjective function are equal.<\/p>\n\n\n\n

Let us learn more about the surjective function, along with its properties and examples.<\/p>\n\n\n\n

What Is a Surjective Function?<\/h2>\n\n\n\n

Surjective function is defined with reference to the elements of the range set, such that every element of the range is a co-domain. A surjective function is a function whose image is equal to its co-domain. Also, the range, co-domain and the image of a surjective function are all equal. Additionally, we can say that a subjective function is an onto function when every y \u2208<\/strong> co-domain has at least one pre-image x \u2208<\/strong> domain such that f(x) = y. Let’s go ahead and explore more about surjective function.<\/p>\n\n\n\n

A function ‘f’ from set A to set B is called a surjective function if for each b \u2208 B there exists at least one a \u2208 A such that f(a) = b. None of the elements are left out in the onto function because they are all mapped from some element of set A. Consider the example given below:<\/p>\n\n\n\n

Let A = {a1<\/sub>, a2<\/sub>, a3<\/sub> } and B = {b1<\/sub>, b2<\/sub> } then f : A \u2192B.:{(a1, <\/sub>b1), <\/sub>(a2<\/sub>, b2<\/sub>), (a3<\/sub>, b2<\/sub>)}<\/p>\n\n\n\n

Here in the above example, every element of set B has been utilized, and every element of set B is an image of one or more than one element of set A.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

In the above examples of functions, the functions which do not have any remaining element in set B is a surjective function. In a surjective function, every element of set B has been mapped from one or more than one element of set A. Also, the functions which are not surjective functions have elements in set B that have not been mapped from any element of set A.<\/p>\n\n\n\n

Properties of Surjective Function<\/h2>\n\n\n\n

A function is considered to be a surjective function only if the range is equal to the co-domain. Here are some of the important properties of surjective function:<\/p>\n\n\n\n

  • In a surjective function, every element in the co-domain will be assigned to at least one element of the domain.<\/li>
  • The co-domain element in a subjective function  can be an image for more than one element of the domain set.<\/li>
  • In a subjective function, the co-domain is equal to the range.A function f: A \u2192B is an onto, or surjective, function if the range of f equals the co-domain of the function f.<\/li>
  • Every function that is a surjective function has a right inverse. Also, every function which has a right inverse can be considered as a surjective function.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"

    A surjective function is defined between set A and set B, such that every element of set B is associated with at least one element of set A. The domain and range of a surjective function are equal. Let us learn more about the surjective function, along with its properties and examples. What Is a Surjective Function? Surjective […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[698],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/19839"}],"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=19839"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/19839\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=19839"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=19839"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=19839"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}