Question

Find gof and fog, if
$\left(i\right)f\left(x\right)=8x^3$ and $g\left(x\right)=x^{\frac{1}{3}}$.

Answer 1

$f\left(x\right)=8x^3$ and $g\left(x\right)=x^{\frac{1}{3}}$
$\therefore \left(gof\right)\left(x\right)=g\left(f\right(x\left)\right)=g\left(8x^3\right)=(8x^3{)}^{\frac{1}{3}}=2x$
and $fog\left(x\right)=f\left(g\right(x\left)\right)=f\left(x^{\frac{1}{3}}\right)=8(x^{\frac{1}{3}}{)}^3=8x$.