1. The problem statement, all variables and given/known data Prove that f(x) = x (for x is rational) if f(x + y) = f(x) + f(y) and f(xy) = f(x)f(y). 2. Relevant equations 3. The attempt at a solution I substituted y = x to get f(2x) = f(2x), which means that you can pull constants out of the function. Therefore, for all x and y, f(xy)=xy and so f(x) = x and f(y) = y. However, I am not sure that this solution works because it seems to simple and illogical in a way. I also didn't prove that x is rational.