Example of function $f:\mathbb R\to \mathbb R$ which is differentible and bijective but its inverse is not differentible.

Question

Example of function $f:\mathbb R\to \mathbb R$ which is differentible and bijective but its inverse is not differentible.

First of all do not know is above is true as for inverse function to be not differentible , there exist some point at which $f'(x)=0$ which is not possible due to bijective ness .

Where I am missing ?

Any Help will be appereciated

https://math.stackexchange.com/questions/2471563/if-f-colon-mathbbr-to-mathbbr-is-one-to-one-and-differentiable-at-a-w?noredirect=1&lq=1 — , Nov 30 '18 at 05:00

score 0 · Answer 1 · answered Nov 30 '18 at 04:59

0

$f'(x)$ can be zero, e.g. $f(x)=x^3$ – user25959 18 mins ago

answered Nov 30 '18 at 04:59

Chris Culter

27,415

Example of function $f:\mathbb R\to \mathbb R$ which is differentible and bijective but its inverse is not differentible.

1 Answers1