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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

`1+x^(5)`

B

`5x^(4)`

C

`(1)/(1+{g(x)}^(5))`

D

`1+{g(x)}^(5)`

Text Solution

AI Generated Solution

To find \( g'(x) \) where \( g \) is the inverse of the function \( f \) and given that \( f'(x) = \frac{1}{1 + x^5} \), we can follow these steps: ### Step 1: Understand the relationship between \( f \) and \( g \) Since \( g \) is the inverse of \( f \), we have: \[ f(g(x)) = x \] ...
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