Question

If the functions $f\left(x\right)\text{and}g\left(x\right)$ are defined by $f\left(x\right)=5x+2;g\left(x\right)=\frac{x-2}{3}$ then find the value of $gof\left(3\right).$

• A. $\frac{1}{3}$
• B. 5
• C. 17
• D. $\frac{11}{3}$

Answer 1

The correct option is B 5

$\text{Given,}f\left(x\right)=5x+2\text{and}g\left(x\right)=\frac{x-2}{3}$
$\because gof\left(x\right)=g\left[f\right(x\left)\right]$
$\therefore gof\left(3\right)=g\left[f\right(3\left)\right]$
$=g\left[5\right(3)+2]=g\left[17\right]=\frac{17-2}{3}=\frac{15}{3}=5$

$\therefore gf\left(3\right)=5$