Let f and g be functions which are differentiable on R. For each of the following statements, determine if it is true or false. If it is true, then prove it. If it is false, then give a counterexample (you must prove that it is indeed a counterexample). (a) If f'(x) = g'(x) for all x, then f(0) = g(0). True False (b) If f'(x) > sin(x) + 2 for all z € R, then there is no solution to the equation ef(x) = 1. O True False (c) If f is strictly increasing and g is strictly decreasing, then both fog and go f are strictly decreasing. O True O False