1. The problem statement, all variables and given/known data Determine whether f: ZxZ->Z is onto if (a) f(m, n) = 2m-n (b) f(m, n) = n^2 - m^2 (c) f(m, n) = m + n + 1 (d) f(m, n) = |m| - |n| (e) f(m, n) = m^2 - 4 2. Relevant equations A function is onto if for every y in the codomain there is at least one X in the domain st f(x) = y 3. The attempt at a solution I have no idea how to start proving this. I know I'm supposed to prove that for every integer y, there is at least 1 (m, n) pair, but that requires solving for another variable m or n doesn't it? This leaves a lot of m,n to test for yes? For example, I can go about the first one by setting m = (y+n)/2 and if y = 0 and n is odd then m is not an integer. However, I know from reading ahead that the first one is onto. For the last one I can do sqrt(y+4) = m If y = 1, then m is not an integer and so y = 1 is not in the range Am I supposed to prove the cases where m is odd, n is even, both are even, both are odd, m is even, n is odd?