- #1
babygotpi
- 3
- 0
Homework Statement
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.