I believe I have the same professor G as mathgirl13 and the whole class is struggling.

I need to prove the converse of the above:

If f: X Y has a two-sided inverse, prove that it is a bijection.

Given and

T.P.

Now choose . This should prove f is injective, right?

Next T.P.

Choose y=f(x) then

but also

This should prove f is surjective, right?

Thanks for any and all help.