A function f is such that f(xy) = f(x + y) for all real values of x and y, and f(5) = 10. What is f(20) + f(−20) equal to?

Setting x = y = 0: f(0) = f(0), trivially true. Setting y = 0: f(0) = f(x) for all x, so f is constant. Since f(5) = 10, we have f(x) = 10 for all x. Hence f(20) + f(−20) = 10 + 10 = 20.