Problem 4. Consider the following pair of functions f N-a).g (aN that map strings of a's to their length, and vice versa f(n)-a g(a)i 4(a) Prove f is a bijection. 4(b) Prove g is a bijection. 4(c) As both functions are bijections, it must be the case that both f and g are invertible. Prove that g is the inverse of f by showing that go f-IN. You may use either set equality or the function equality method to show they are equal The notation IN is the identity function for N. IN N-N defined by IN(x). The function g o f(x)g(f(x (see lecture notes on function composition)