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 ).

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- Feb 16th 2011, 10:28 PM #1

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## diffeomorphism

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.

- Feb 16th 2011, 10:51 PM #2

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- Feb 16th 2011, 10:54 PM #3

For example,

Fernando Revilla