Question

If $f\left(x\right)=|x-2|$ and $g\left(x\right)=f\left(f\right(x\left)\right)$, then $\frac{dg\left(x\right)}{dx}$ for $x>10$ is

• A. $1$ or $-1$
• B. $1$
• C. $-1$
• D. None of these

Answer 1

The correct option is B $1$

Given, $f\left(x\right)=|x-2|$ and $g\left(x\right)=f\left(f\right(x\left)\right)$
$\therefore g\left(x\right)=||x-2|-2|$
For $x>10$
$g\left(x\right)=\left|\right(x-2)-2|=x-4$
$\therefore \frac{dg\left(x\right)}{d\left(x\right)}=1$