Question

$f\left(x\right)=|x-2|andg\left(x\right)=f(f(x\left)\right)$, $x>20$, then $g\text{'}\left(x\right)=$

• A. $1$
• B. $0$
• C. $9$
• D. $18$

Answer 1

The correct option is A

$1$

Explanation for the correct option.:

Differentiation of composite function:

In, $f\left(x\right)=|x-2|$, it is given that $x>20$, so $f\left(x\right)=x-2$.

Now,

$\begin{array}{rcl}g\left(x\right)& =& f(f(x\left)\right)\\ & =& f\left(x\right)-2\\ & =& x-2-2\\ & =& x-4\end{array}$

So, $g\text{'}\left(x\right)=1$

Hence, option A is correct.