Looking for help with a textbook problem.

Give an example to demonstrate that a one-to-one and onto mapping need not be a diffeomorphism. (Hint: Take $\displaystyle m=n=1$)

I'm assuming that the hint means let $\displaystyle F: R^1 \rightarrow R^1$

I'm very stuck, however and having trouble thinking this through. Help and/or a couple of examples would be greatly appreciated.