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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 x. 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

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To solve the problem, we need to find \( g''(f(x)) \) where \( g(x) \) is the inverse of the differentiable function \( f(x) \). ### Step-by-Step Solution: 1. **Understanding the relationship between \( g(x) \) and \( f(x) \)**: Since \( g(x) \) is the inverse of \( f(x) \), we have: \[ g(f(x)) = x ...
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