Answer
Thus we see that, $\color{blue}{\bf{ ( f \text{ }\omicron\text{ g} )(x) = ( g \text{ }\omicron\text{ f} )(x) =x }}$
Work Step by Step
We are given the two functions $\bf{f}$ and $\bf{g}$
$\bf{f(x) = \sqrt[3]{x+1} }$ and $\bf{g(x) = x^3-1 }$
we are asked to show that $\bf{ ( f \text{ }\omicron\text{ g} )(x) = ( g \text{ }\omicron\text{ f} )(x) =x }$
$ ( f \text{ }\omicron\text{ g} )(x)=( g \text{ }\omicron\text{ f} )(x) $
$ \sqrt[3]{x^3-1+1} = ( \sqrt[3]{x+1} )^3-1 $
$ x-1+1 = x+1-1 $
$ x = x $
Thus we see that, $\color{blue}{\bf{ ( f \text{ }\omicron\text{ g} )(x) = ( g \text{ }\omicron\text{ f} )(x) =x }}$
