A function is bijective if it is both injective and surjective. A bijective function f:A → B has an inverse function, f-1: B → A, such that for all a in A, f-1(f(a)) = a, and for all b in B, f(f-1(b)) = b.
It is worth noting that since for every function f there exists a similar function g such that g(x) = f(x) for every x in the domain, and the range of g is restricted to the codomain (and so is surjective), every injective function has a corresponding function g-1 such that for all a in A, g-1(f(a)) = a, and for all c in the codomain of f, f(g-1(c)) = c. This function is very nearly the inverse of f, except the domain of g-1 is the codomain of f, rather than the domain of f.