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If f (x) =|x-1|and g (x) =f (f (f (x))),...

If `f (x) =|x-1|and g (x) =f (f (f (x))),` then `g' (x)` is equal to:

A

22

B

20

C

18

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`f(0)=5 and underset(x to 0)lim (f(x)-5)/(x)-4`
`therefore underset(x to 0)lim (f(x)-5)/(x)=4`
`therefore underset(x to 0)lim (f(x)-f(0))/(x)=4Rightarrow f'(0)=4`
Now,
`g(x)=(x^(2)+2x+3)f(x)`
`Rightarrow g'(x)=(2x+2)f(x)+(x^(2)+2x+3)f'(x)`
`Rightarrow g'(0)=2f(0)+3f'(0)=2xx5+3xx4=22`
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OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Section I - Solved Mcqs
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  16. Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x l...

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  17. Check the continuity of f(x) = {{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+...

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