Def. Let f : X Y 1. A left inverse off is a function g : Y X such that, for all x X, g(f(x)) = z. 2. A right inverse of f is a function g : Y X such that, for all y E Y, f(g(y))-y. 3. An inverse of f is a function that is both a left inverse and a right inverse of f Theorem! 1. A function f : X Y has an inverse if and only if it is both one-to-one and onto. Prove Theorem 1