Hello yvonnehrYour proof is fine (I take it should be ), but I think you can simplify it a bit.

You don't really need to say anything about at all for the 'onto' proof. (You're not trying to divide anything by zero, are you? And , which is OK.)

So I think all you really need to say is:

is even and

is onto.

And your counterexample ( ) is all you need to prove that is not one-to-one.

Grandad