# Surjective function

From Citizendium

In mathematics, a **surjective function** or **onto function** or **surjection** is a function for which every possible output value occurs for one or more input values: that is, its image is the whole of its codomain.

An surjective function *f* has an inverse (this requires us to assume the Axiom of Choice). If *y* is an element of the image set of *f*, then there is at least one input *x* such that . We define to be one of these *x* values. We have for all *y* in the codomain.