Question

$\text{If}f\left(x\right)=2x^2\text{and}g\left(x\right)=\frac{1}{3x},\text{then}fog\text{is}$___

• A. $\frac{2}{3x^2}$
• B. $\frac{2}{9x^2}$
• C. $\frac{3}{2x^2}$
• D. $\frac{1}{6x^2}$

Answer 1

The correct option is B $\frac{2}{9x^2}$

Given: $f\left(x\right)=2x^2\text{and}g\left(x\right)=\frac{1}{3x}$
$fog=f\left(g\right(x\left)\right)=f\left(\frac{1}{3x}\right)=2\left(\frac{1}{(3x{)}^2}\right)$
$=\frac{2}{9x^2}$

$\therefore fog=\frac{2}{9x^2}$