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If g is the inverse of a function f and ...

If g is the inverse of a function f and `f'(x)=(1)/(1+x^(5)),` then g'(x) is equal to

A

`1+x^(5)`

B

` 5x^(4)`

C

` 1/(1+{g(x)}^(5))`

D

`1+{g(x)}^(5)`

Text Solution

Verified by Experts

The correct Answer is:
D
Here, g is the inverse of f(x) .
` rArr" " fog (x) = x `
On differentiating w.r.t. x, we get
`f'{g(x)}xxg'(x) = 1 rArr g'(x)= 1/(f'(g(x)))`
` = 1/(1/(1+{g(x)}^(5)))" "[:' f'(x) = 1/(1+x^(5))]`
` rArr" " g'(x) = 1+{g(x)}^(5)`
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