Example of function $f:mathbb Rto mathbb R$ which is differentible and bijective but its inverse is not...
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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 '18 at 4:38
MathLoverMathLover
51410
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add a comment |
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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 '18 at 4:38
MathLoverMathLover
51410
$endgroup$
3
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$f'(x)$ can be zero, e.g. $f(x)=x^3$
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– user25959
Nov 30 '18 at 4:40
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math.stackexchange.com/questions/2471563/…
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– d.k.o.
Nov 30 '18 at 5:00
add a comment |
$begingroup$
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 '18 at 4:38
MathLoverMathLover
51410
$endgroup$
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 '18 at 4:38
MathLoverMathLover
51410
asked Nov 30 '18 at 4:38
MathLoverMathLover
51410
asked Nov 30 '18 at 4:38
MathLoverMathLover
51410
asked Nov 30 '18 at 4:38
MathLoverMathLover
51410
asked Nov 30 '18 at 4:38
MathLoverMathLover
51410
51410
3
$begingroup$
$f'(x)$ can be zero, e.g. $f(x)=x^3$
$endgroup$
– user25959
Nov 30 '18 at 4:40
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math.stackexchange.com/questions/2471563/…
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– d.k.o.
Nov 30 '18 at 5:00
add a comment |
3
$begingroup$
$f'(x)$ can be zero, e.g. $f(x)=x^3$
$endgroup$
– user25959
Nov 30 '18 at 4:40
$begingroup$
math.stackexchange.com/questions/2471563/…
$endgroup$
– d.k.o.
Nov 30 '18 at 5:00
3
3
$begingroup$
$f'(x)$ can be zero, e.g. $f(x)=x^3$
$endgroup$
– user25959
Nov 30 '18 at 4:40
$begingroup$
$f'(x)$ can be zero, e.g. $f(x)=x^3$
$endgroup$
– user25959
Nov 30 '18 at 4:40
$begingroup$
math.stackexchange.com/questions/2471563/…
$endgroup$
– d.k.o.
Nov 30 '18 at 5:00
$begingroup$
math.stackexchange.com/questions/2471563/…
$endgroup$
– d.k.o.
Nov 30 '18 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
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$f'(x)$ can be zero, e.g. $f(x)=x^3$ – user25959 18 mins ago
answered Nov 30 '18 at 4:59
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Chris Culter
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$f'(x)$ can be zero, e.g. $f(x)=x^3$
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– user25959
Nov 30 '18 at 4:40
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math.stackexchange.com/questions/2471563/…
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– d.k.o.
Nov 30 '18 at 5:00