injectivity and surjectivity (onto and one-one)

I was going over my assignment to study for the upcoming midterm, and I thought I had a grasp on surjectivity and injectivity...I don't. Can someone tell me where I went wrong in proving these to 'jectives'.

define g:integers -> integers be defined by g(n)=4n-5. is it injective? surjective?

I wrote:

Injective:

Suppose g(n)=g(m)

4n-5=4m-5

4n=4m

n=m therefor it is injective

Surjective:

let f(a)=b

4a -5=b

a=(b+5)/4

sub back into the equation g(a)=4a-5 to get 4[(b+5)/4]-5

=b+5-5

=b, so therefor it is surjective

I think this is correct, but he wrote something along the lines of f(x)=2 has no solution in integers. This is true, so why does my way of doing surjectivity not work. What am I doing or assuming wrong?