1. The problem statement, all variables and given/known data Suppose that a function f R->R has the property that f(u+v) = f(u)+f(v). Prove that f(x)=f(1)x for all rational x. Then, show that if f(x) is continuous that f(x)=f(1)x for all real x. 3. The attempt at a solution I've proved that f(x)=f(1)x for all natural x by breaking up x into f(1)+f(x-1) and using induction, but I can't figure out how to do it for all rationals.