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If g is inverse of fand f'(x)=(1)/(1+x^(...

If g is inverse of fand `f'(x)=(1)/(1+x^(n))`, then g'(x) equals

A

`(1)/(1+(g(x)^(n)))`

B

`1+(g(x)^(n))`

C

`(g(x)^(n))-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Since g is the inverse of function f. Therefore, fog(x)=gof(x)=x for all x.
`Rightarrow (d)/(dx)(fog(x))=1" for all x"`
`Rightarrow f'(g(x))g'(x)=1"for all x"`
`Rightarrow (1)/(1+(g (x))^(n)), g'(x)=1 Rightarrow g'(x)=1+(g (x))^(2)`
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OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
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  6. On the interval I = [-2, 2], if the function f(x) = {{:((x+1)e^(-((1)/...

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  7. If f(x)={{:(,(|x+2|)/(tan^(-1)(x+2)),x ne -2),(,2, x=-2):}, then f(x) ...

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  8. Let f(x)=(x+|x|)|x| . Then, for all x f is continuous

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  12. If f(x)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1] ...

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  13. If f(x) = sin ^(-1)((2x)/(1 + x^(2))) then f (x) is differentiable in ...

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  15. If f(x)=|x-a|varphi(x), where varphi(x) is continuous function, then f...

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  16. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)+. . . . +(x^2)/((1+x^2)^n)...

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  19. If f(x)=|log(e)|x||," then "f'(x) equals

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  20. Let f(x)={1/(|x|)\ \ \ \ \ for\ |x|geq1a x^2+b\ \ \ \ \ \ \ \ for\ |x|...

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  21. Let h(x)="min "{x,x^(2)} for every real number of x. Then, which one o...

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