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Let f:""(1,""1)vecR be a differentiable ...

Let `f:""(1,""1)vecR` be a differentiable functio with `f(0)""=""-1""a n d""f'(0)""=""1` . Let `g(x)""=""[f(2f(x)""+""2)]^2` . Then `g'(0)""=` (1) `4` (2) 0 (3) `2` (4) -4

A

-2

B

4

C

-4

D

0

Text Solution

AI Generated Solution

To find \( g'(0) \) for the function \( g(x) = [f(2f(x) + 2)]^2 \), we will follow these steps: ### Step 1: Differentiate \( g(x) \) Using the chain rule, we differentiate \( g(x) \): \[ g'(x) = 2[f(2f(x) + 2)] \cdot f'(2f(x) + 2) \cdot (2f'(x)) ...
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