Question

If $f\left(x\right)=|x-8|$ & $g\left(x\right)=f\left(f\right(x\left)\right)$ for all $x>16$ then $g^{\prime }\left(x\right)$ equals

• A. $1$
• B. $-1$
• C. $0$
• D. $1$ or $-1$ depending on the value of $x$

Answer 1

The correct option is A $1$

For x>16
$|x-8|$
$=x-8$
$g\left(x\right)=f\left(f\right(x\left)\right)$
For $x>16$,
$\Rightarrow g\left(x\right)=x-16$
$\Rightarrow g^{\prime }\left(x\right)=1$