A function f : [0, 1] - [0, 1] is said to have a fixed point if there exists a * 6 0, 1 such that f (a*) = x*. (a) Prove that if f : [0, 1] - [0, 1] is continuous, then f (x) has a fixed point. [4 marks] (b) Suggest an example of a discontinuous function g : [0, 1] -> [0, 1] without a fixed point. Justify why it does not have a fixed point? [2 marks] (c) Let f : [0, 1] - [0, 1] . If there exists two fixed points a* and w*, such that f (2*) =x* and f (w*) = w*, is it true that x* = w*? Justify your answer. [2 marks]