Question

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

• A. 1
• B. -1
• C. 0
• D. 2

Answer 1

The correct option is C 0

$f\left(x\right)=x-8$ $x\ge 8$

$8-x$ $x<8$

$\Rightarrow \forall x>16\Rightarrow f\left(x\right)=x-8$

$\therefore g\left(x\right)=f\left(f\right(x\left)\right)$

$=|x-(x-8)|$

$=|8|$

$g\left(x\right)=8$

$\therefore g^{\prime }\left(x\right)=0$