jmc

Question

The function f(x) satisfies f(x + y) = f(x) + f(y) + 2xyfor all real numbers x and y. If f(1) = 4, then find f(8).

Accepted Answer

Setting x = y, we get f(2x) = 2f(x) + 2x^2.Then align* f(2) &= 2f(1) + 2 1^2 = 10, f(4) &= 2f(2) + 2 2^2 = 28, f(8) &= 2f(4) + 2 4^2 = 88. align*