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"f"("x") = "x"3 is not a diffeomorphism from r to itself because its derivative vanishes at 0 (and hence its inverse is not differentiable at 0).
"f"("x") = "x"3, for example, is not a diffeomorphism from r to itself because its derivative vanishes at 0 (and hence its inverse is not differentiable at 0).
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