The function g is called an inverse to the function f if the domain of g is the range of f, if g(f(x)) = x for every x in the domain of f and if f(g(y)) = y for each y in the range of f.
(a) Explain why a function is a bijection if and only if it has an inverse function.
(b) Explain why a function that has an inverse function has only one inverse function.