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

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

Verified by Experts

`g'(x)=2[f(2f(x)+2)][(d)/(dx)(f(2f(x)+2))]`
`=2[f(2f(x)+2)][f'(2+f(x)+2)xx2f'(x)]`
`rArr" "g'(0)=2f(2f(0)+2)f'(2f(0)+2)2f'(0)`
`=4f(0)[f'(0)]^(2)`
`4(-1)(1)=-4`

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