A function $f: X \to Y$ is bijective (both injective and surjective) if and only if it has an inverse $f^{-1} : Y\to X$ (a function that is both a left-inverse and a right-inverse). We prove this biconditional result here.
A function $f: X \to Y$ is bijective (both injective and surjective) if and only if it has an inverse $f^{-1} : Y\to X$ (a function that is both a left-inverse and a right-inverse). We prove this biconditional result here.