# Example:Surjections and solving equations

One way of understanding surjections and right inverses is as the existence of a solution to an equation. For example, the function given by is not surjective. This is reflected in the fact that you cannot solve the equation for an arbitrary ; indeed, there is no with .

If we restrict the codomain of so that the function becomes surjective (i.e. let ), then there is a right inverse (namely the function).