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Suppose g is the inverse fiunction of a ...

Suppose g is the inverse fiunction of a diffdifferentiable finction fand `G(x)=(-4)/(g^2(x)).` If `f(5)=3 and f'(5)=1/125` then `g;(3)` is equal to

A

1

B

2

C

4

D

8

Text Solution

Verified by Experts

The correct Answer is:
A
`f(5)=3rArrg(3)=5`
`g'(y)=(1)/(f'(x))rArrg'(3)=(1)/(f'(5))=125`
`G'(x)=((-4)(-2))/(g^(3)(x)).g'(x)`
`G'(3)=(8)/(g^(3)(x))g'(x)=(8)/(125)xx125=8`.
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