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 [math]f(x) := sin(x) [/math] is not surjective. This is reflected in the fact that you cannot solve the equation [math]f(x) = y [/math] for an arbitrary [math]y [/math]; indeed, there is no [math]x [/math] with [math]f(x) = 7 [/math].

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