2. Let f : R → R be a continuous function. Suppose that (f o f) (x) = x for every x E R. (a) Prove that there exists a point c ER such that f (c) Hint: Consider the function g (x) = f (x) – x for...

Extracted text: 2. Let f : R → R be a continuous function. Suppose that (f o f) (x) = x for every x E R. (a) Prove that there exists a point c ER such that f (c) Hint: Consider the function g (x) = f (x) – x for every x € R. = C. (b) Give an example for a function satisfying the above requirements, and such that f id, -id , where id is the identity function.