Question

If $f:R\to R$ is defined by $f\left(x\right)=3x-2$ then $\left(fof\right)\left(x\right)+2=$

• A. $f\left(x\right)$
• B. $2f\left(x\right)$
• C. $3f\left(x\right)$
• D. $-f\left(x\right)$

Answer 1

The correct option is B $2f\left(x\right)$

$f\left(x\right)=3x-2$

$f\left(f\right(x)=3(3x-2\left)\right)-2$

$=9x-6-2$

$=9x-8$

$f\left(f\right(x\left)\right)+2=9x-8+2$

$=9x-6$

$=3(3x-2)$

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