Example of function $f:mathbb Rto mathbb R$ which is differentible and bijective but its inverse is not...
Example of function $f:mathbb Rto mathbb R$ 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
real-analysis derivatives
asked Nov 30 at 4:38
MathLover
45710
add a comment |
Example of function $f:mathbb Rto mathbb R$ 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
real-analysis derivatives
asked Nov 30 at 4:38
MathLover
45710
3
$f'(x)$ can be zero, e.g. $f(x)=x^3$
– user25959
Nov 30 at 4:40
math.stackexchange.com/questions/2471563/…
– d.k.o.
Nov 30 at 5:00
add a comment |
Example of function $f:mathbb Rto mathbb R$ 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
real-analysis derivatives
asked Nov 30 at 4:38
MathLover
45710
Example of function $f:mathbb Rto mathbb R$ 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
real-analysis derivatives
real-analysis derivatives
asked Nov 30 at 4:38
MathLover
45710
asked Nov 30 at 4:38
MathLover
45710
asked Nov 30 at 4:38
MathLover
45710
asked Nov 30 at 4:38
MathLover
45710
asked Nov 30 at 4:38
MathLover
45710
45710
3
$f'(x)$ can be zero, e.g. $f(x)=x^3$
– user25959
Nov 30 at 4:40
math.stackexchange.com/questions/2471563/…
– d.k.o.
Nov 30 at 5:00
add a comment |
3
$f'(x)$ can be zero, e.g. $f(x)=x^3$
– user25959
Nov 30 at 4:40
math.stackexchange.com/questions/2471563/…
– d.k.o.
Nov 30 at 5:00
3
3
$f'(x)$ can be zero, e.g. $f(x)=x^3$
– user25959
Nov 30 at 4:40
$f'(x)$ can be zero, e.g. $f(x)=x^3$
– user25959
Nov 30 at 4:40
math.stackexchange.com/questions/2471563/…
– d.k.o.
Nov 30 at 5:00
math.stackexchange.com/questions/2471563/…
– d.k.o.
Nov 30 at 5:00
add a comment |
1 Answer
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$f'(x)$ can be zero, e.g. $f(x)=x^3$ – user25959 18 mins ago
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$f'(x)$ can be zero, e.g. $f(x)=x^3$ – user25959 18 mins ago
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$f'(x)$ can be zero, e.g. $f(x)=x^3$ – user25959 18 mins ago
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$f'(x)$ can be zero, e.g. $f(x)=x^3$ – user25959 18 mins ago
$f'(x)$ can be zero, e.g. $f(x)=x^3$ – user25959 18 mins ago
answered Nov 30 at 4:59
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$f'(x)$ can be zero, e.g. $f(x)=x^3$
– user25959
Nov 30 at 4:40
math.stackexchange.com/questions/2471563/…
– d.k.o.
Nov 30 at 5:00