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If f(x)=x+tanx and g(x) is inverse of f(...

If `f(x)=x+tanx` and `g(x)` is inverse of `f(x)` then `g^(')(x)` is equal to

A

`1/(1+(g(x)-^(2))`

B

`1/(2+(g(x)-x)^(2))`

C

`1/(1-(g(x)-x)^(2))`

D

`1/(2-(g(x)-x)^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
`g=f^(-1)(x)impliesf(g(x))=x`
`f^(')g(x).g^(')(x)=1`
`impliesg^(')(x)=1/(1+sec^(2)g(x))=1/(2+tan^(2)g(x))`
`g^(')(x)=1/(2+(f(g(x))-g(x))^(2))=1/(2+(x-g(x))^(2))`
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