Take F(x)= x/(x+1) for x in [0,1] and F(x)=x for x>1.
(reflect this to the negative side).
I believe it's injective and onto, but F its derivative at x=1 isn't defined.
( and ).
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 )
I'm assuming that the hint means let
I'm very stuck, however and having trouble thinking this through. Help and/or a couple of examples would be greatly appreciated.