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Let f:RtoR be defined as f(x)=(2x-3pi)^(...

Let `f:RtoR` be defined as `f(x)=(2x-3pi)^(3)+(4)/(3)x+cosx` and `g(x)=f^(-1)(x)` then

A

`g^(')(2pi)=(3)/(7)`

B

`g^(')(2pi)=(7)/(3)`

C

`g^('')(2pi)=0`

D

`g^('')(2pi)=-(27)/(243)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`f((3pi)/(2))=2pi`
`becauseg(2pi)=(3pi)/(2)`
`g(f(x))=x`
`impliesg^(')(2pi)=(1)/(f'((3pi)/(2)))=(3)/(7)`
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