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If g(x) is the inverse function of f(x) and `f'(x)=(1)/(1+x^(4))`, then `g'(x)` is

A

`1 + [g(x)]^(4)`

B

`1- [g(x)]^(4)`

C

`1+[f(x)]^(4)`

D

`1/(1+[g(x)]^(4))`

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `g(x) = f'(x)`
`f(g(x)) =x`
On differentiating both sides w.r.t. `'x'` we get
`f'(g(x)) .g'(x) = 1`
`:. (1)/(1+(g(x))^(4)) g'(x) = 1`
[ `:' f'(x) = 1/(1+x^(4))`(given)]
`rArr g'(x) = 1 +[g(x))]^(4)`
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