Confusing Surjective Question

Quote:

Let

Let

for all

.

Show

is injective but not surjective.

Did this easily, injective was simple enough, and showed that

Quote:

For which element

of

is it true that there's a bijective function

such that

for all

.

No idea where to start with this, obviously need to show that this new function is now surjective as well as injective, but not sure how to do this seeing as I just proved that an extremely similar function isn't surjective!!

Any help would be greatly appreciated.