In mathematics, if ƒ is a function from A to B then an inverse function for ƒ is a function in the opposite irection, from B to A, with the property that a round trip (a composition) from A to B to A (or from B to A to B) returns each element of the initial set to itself. Thus, if an input x into the function ƒ produces an output y, then inputting y into the inverse function ƒ–1 produces the output x. Not every function has an inverse; those that do are called invertible.