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If g is the inverse of a function f and `f^'(x)=1/(1+x^5)` then g(x) is equal to (1) `1""+x^5` (2) `5x^4` (3) `1/(1+{g(x)}^5)` (4) `1+{g(x)}^5`

A

`1+x^(5)`

B

`5x^(4)`

C

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

D

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

Text Solution

Verified by Experts

Since g is inverse of f,f(g(x))=x
`rArr" "f'(g(x))g'(x)=1`
`rArr" "g'(x)=1+(g(x))^(5)" "(becausef'(x)=(1)/(1+x^(5)))`
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