hello!

I am trying to work this out, not sure where to start even though the theorem appears intuitive! I thought I had proven it but then realised I has assumed the existance of an inverse!

For functions f,g and sets A, B

Given and and

where is the function

Then exists and

To show the exsistance of an inverse requires that f is a bijection? not sure how to derive that from what is given.

Thanks in advance!