(a) (i) Explain why there can be no continuous function f [0, 1] (0,1) that is a surjection. (ii) Give an example of a continuous surjection g: (0, 1) [0, 1]. (b) (i) (ii) [5] State the Mean Value Theorem. Let f: RR be a differentiable function, whose derivative f' is continuous. Let a ER be a point for which f(a) = 0 but f'(a) 0. Use the Mean Value Theorem to show that there exists > 0 such that f(x) #0 whenever 0 < x-a