Let f : Z × Z → Z × Z be defined as f(m, n) = (3m + 7n, 2m + 5n). Is f a bijection, i.e.,one- to-one and onto? If yes then give a formal proof, based on the definitions of one-to-oneand onto, and derive a formula for f−1. If no then explain why not.

I did:

assume f(m1,n1) = f(m2,n2)
and I just equated both side of the equation making a sys. of equations and finding that m1 = m2 and n1=n2 making it one to one.

However I can't prove how it is onto, any help?

Question

Let f : Z × Z → Z × Z be defined as f(m, n) = (3m + 7n, 2m + 5n). Is f a bijection, i.e.,one- to-one and onto? If yes then give a formal proof, based on the definitions of one-to-oneand onto, and derive a formula for f−1. If no then explain why not.

I did: 

assume f(m1,n1) = f(m2,n2)
and I just equated both side of the equation making a sys. of equations and finding that m1 = m2 and n1=n2 making it one to one. 

However I can't prove how it is onto, any help?