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.