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If f(x) = x + tan x and f is the inverse...

If `f(x) = x + tan x` and `f` is the inverse of `g`, then `g'(x)` is equal to

A

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

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=x+tan x`
`therefore" "f(f^(-1)(y))=f^(-1)(y)+tan f^(-1)(y)`
`"or "y=g(y)+tan g(y)`
`"or "x=g(x)+tan g(x)`
Differentiating, we get `1=g'(x)+sec^(2)g(x)g'(X)`
`"or "g'(x)=(1)/(1+sec^(2)g(x))=(1)/(2+[g(x)-x]^(2))`
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