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.
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