Let f:R->R such that f(x+y) = f(x)f(y), f(x) is differentiable at x = 0, and f(x) is not identically 0. a) Prove that f(0) = 1 b) Prove that f(x) is differentiable at every point x and that f'(x) = f(x)f(0). c) Let g(x) = f(x) - e^(cx) where c = f'(0). Prove that g(x) satisfies the differential equation g'(x) = cg(x) with initial condition g(0) = 0. d) Solve the differential equation and prove that g(x) is identically 0. This is for my Analysis I class, and I am so lost, any help is greatly appreciated thank you.