jmc

Question

The function f(x) satisfies f(x + y) = f(x) + f(y)for all real numbers x and y, and f(4) = 5. Find f(5).

Accepted Answer

We can write align* f(4) &= f(3) + f(1) &= f(2) + f(1) + f(1) &= f(1) + f(1) + f(1) + f(1), align*so 4f(1) = 5, which means f(1) =54. Therefore, f(5) = f(1) + f(4) = 5 + 54 = 254.