2. PAST PAPER QUESTION (2018): Let f be a function that satisfies the following properties: f(x + y) - f(x)f(y) for allx, y E R, and f'(0) - 1. a. Explain why f is continuous at r - 0). b. Show the following two facts: that f(0) - 1, and that f(x) / 0 for all r e R. ( You may prove them in either order, and use whichever you prove first to prove the second if you wish. ) c. Show that f is continuous for all r C R. d. Show that f is differentiable for all r e R, and compute f'(r) in terms of r and f(r). e. In fact, f is uniquely defined by the above properties, and is a well-known function. Which is it