[SOLVED] functions on rational numbers 1. The problem statement, all variables and given/known data Find all functions from Q to Q which satisfy the following two conditions: i)f(1)=2 ii)f(xy)=f(x)f(y)-f(x+y)+1 for all x,y in Q 2. Relevant equations 3. The attempt at a solution I can show by integers that if x is an integer, then f(x)=x+1. However, I am having trouble getting the value of the function for rational numbers. I want to do induction on n to get the inverse integers 1/n, but I cannot get 1/2. There is probably something clever you can plug in for x and y to get f(1/2), but I can't think of it.