4th Balkan Mathematical Olympiad Problems 1987

4th Balkan Mathematical Olympiad Problems 1987A1.  f is a real valued function on the reals satisfying (1) f(0) = 1/2, (2) for some real a we have f(x+y) = f(x) f(a-y) + f(y) f(a-x) for all x, y. Prove that f is constant.