jmc

Question

The function f(x) satisfies b^2 f(a) = a^2 f(b)for all real numbers a and b. If f(2) 0, find f(5) - f(1)f(2).

Accepted Answer

Setting a = 5 and b = 2, we get 4f(5) = 25f(2),so f(5)f(2) = 254. Setting a = 1 and b = 2, we get 4f(1) = f(2),so f(1)f(2) = 14. Hence, f(5) - f(1)f(2) = 254 - 14 = 6.