Limit Continuity And Differentiability Ques 16

  1. If $f(x)=|x-2|$ and $g(x)=f[f(x)]$, then $g^{\prime}(x)= ………$ for $x>2$.

(1990, 2M)

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Answer:

Correct Answer: 16.$(1)$

Solution: Given, $\quad f(x)=|x-2|$

$\therefore \quad g(x)=f[f(x)]=| x-2|-2|$

When, $ x>2 $

$g(x)=|(x-2)-2|=|x-4|=x-4$

$\therefore \quad g(x)=1$ when $x>2$



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