1. The problem statement, all variables and given/known data See attatchment. I couldn't upload the picture. 2. The attempt at a solution I have the following: Define mapping f: ℝ2 -> ℝ as follows: f(x,y) = 3x - 4y Claim: f is a homomorphism Pick any (x,y) in ℝ2. Then f(x,y) = f(x)*f(y) = 3x - 4y = (x+x+x)-(y+y+y+y) = x+x+x-y-y-y-y = f(x*y). Hence, it perserves the operation. Claim: f is onto. Pick any (x,y) in ℝ2 such that (x,y) = (1,0). Then... I don't think I'm going the right way on showing f is onto.