For the function f : ℝ -> ℝ it's true that : f(x + y) = f(x)*f(y) , for every x, y∈ℝ and that f(0) ≠ 0 Prove that : a) f(x) ≠ 0 , for every x∈ℝ b) f(x) > 0 , for every x∈ℝ c) f(0) = 1 d) f(x)*f(-x) = 1 , for every x∈ℝ e) If the function f(x) = 1 has a single solution, then the f can be inversed and it's true that [tex]f ^{ - 1} (xy) = f^{ - 1}(x) \: + \: f^{ - 1}(y) [/tex] for every x , y > 0