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If g is the inverse of a function f and `f^'(x)=1/(1+x^5)` then g(x) is equal to (1) `1""+x^5` (2) `5x^4` (3) `1/(1+{g(x)}^5)` (4) `1+{g(x)}^5`

A

`-((d^(2)y)/(dx^(2)))((dy)/(dx))^(-3)`

B

`((d^(2)y)/(dx^(2)))^(-1)`

C

`-((d^(2)y)/(dx^(2)))^(-1)((dy)/(dx))^(-3)`

D

`((d^(2)y)/(dx^(2)))((dy)/(dx))^(-2)`

Text Solution

AI Generated Solution

To solve the problem, we need to find the expression for \( g(x) \), where \( g \) is the inverse of the function \( f \) and we are given that \( f'(x) = \frac{1}{1 + x^5} \). ### Step-by-step Solution: 1. **Understanding the relationship between \( f \) and \( g \)**: Since \( g \) is the inverse of \( f \), we have the relationship: \[ f(g(x)) = x ...
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