Question

If $f\left(x\right)=(x-1)+(x+1)$ and
$g\left(x\right)=f\left\{f\right(x\left)\right\}$ then $g^{\prime }\left(3\right)$

• A. equals $1$
• B. equals $0$
• C. equals $3$
• D. equals $4$

Answer 1

The correct option is D equals $4$

Simplifying,$f\left(x\right)$ we get

$f\left(x\right)=2x$

Hence

$f\left(f\right(x\left)\right)=2\left(f\right(x\left)\right)$

$=2\left(2x\right)$

$=4x$

Hence

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

$=4x$

Thus

$g^{\prime }\left(x\right)=4$

Hence $g^{\prime }\left(3\right)=4$ .