Surjective Function

A surjective function is a function whose image is equal to its codomain. Equivalently, a function f with domain X and codomain Y is surjective if for every y in Y there exists at least one x in X with . Surjections are sometimes denoted by a two-headed rightwards arrow, as in f : X ↠ Y.

Symbolically,

Let, then is said to be surjective if