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Let g(x) be the inverse of an invertible...

Let `g(x)` be the inverse of an invertible function `f(x),` which is differentiable for all real `xdot` Then `g''(f(x))` equals.

A

`-(f''(x))/((f'(x))^(3))`

B

`(f'(x)f''(x)-(f(x))^(3))/(f'(x))`

C

`(f'(x)f''(x)-(f'(x))^(2))/((f'(x))^(2))`

D

none of these

Text Solution

Verified by Experts

`"Given that "g^(-1)(x)=f(x)`
`"or "x=g(f(x))`
`"or "g'(f(x))f'(x)=1`
`"or "g'(f(x))=(1)/(f'(x))`
`"or "g''(f(x))f'(x)=(-f''(x))/([f'(x)]^(2))`
`"or "g''(f(x))=(-f''(x))/([f'(x)]^(3))`
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