Find \operatorname{gof} and f o g if f(x)=8 x^{3} and g(x)=x^{\frac{1}{3}}

Given, \mathrm{f}(\mathrm{x})=8 \mathrm{x}^{3} and \mathrm{g}(\mathrm{x})=\mathrm{x}^{1 / 3}
( gof )(x)=g[f(x)]=g\left(8 x^{3}\right)=g(y), where y=8 x^{3}

    \[=\mathrm{y}^{1 / 3}=\left(8 \mathrm{x}^{3}\right)^{1 / 3}=2 \mathrm{x}\]

( fog )(\mathrm{x})=\mathrm{f}[\mathrm{g}(\mathrm{x})]=\mathrm{f}\left(\mathrm{x}^{1 / 3}\right)=\mathrm{f}(\mathrm{y}), where \mathrm{y}=\mathrm{x}^{1 / 3}

    \[=8 \mathrm{y}^{3}=8\left(\mathrm{x}^{1 / 3}\right)^{3}=8 \mathrm{x}\left(\frac{1}{3} \times 3\right)=8 \mathrm{x}\]