Determine all functions f: R → R that f (x + y) + f (x-y) = 2f (x) + 2f (y) para any real x, y.

Step-by-step explanation:

A function f : R → R + satisfies f (x + y) = f (x). f (y) Vxe R. If f (0) = 2, then show that f (x) = 2f (x). 2. Let f (xy) = f (x) f (y) V x, ye R and f (1) # 0, f' (1) = 1, prove that fis differentiable for all x + 0. Hence determine f (x). X + f (x) + f 3. Let f * regio for real x and y.