Answer
$\color{blue}{\bf{ ( f \text{ }\omicron\text{ g} )(x) = ( g \text{ }\omicron\text{ f} )(x) =x }}$
Work Step by Step
We are given the two functions $\bf{f}$ and $\bf{g}$
$\bf{f(x) = \sqrt[3] {5x+4} }$ and $\bf{g(x) = \dfrac{1}{5}x^3-\dfrac{4}{5} }$
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] {5(\dfrac{1}{5}x^3-\dfrac{4}{5} )+4} = \dfrac{1}{5}( \sqrt[3] {5x+4})^3-\dfrac{4}{5} $
$ \sqrt[3] {\dfrac{5}{5}x^3-\dfrac{20}{5} +4} = \dfrac{1}{5}( {5x+4})-\dfrac{4}{5} $
$ \sqrt[3] {1x^3-4 +4} = \dfrac{5}{5}x+ \dfrac{4}{5}-\dfrac{4}{5} $
$ \sqrt[3] {x^3} = 1x +0 $
$ x = x $
Thus we see that, $\color{blue}{\bf{ ( f \text{ }\omicron\text{ g} )(x) = ( g \text{ }\omicron\text{ f} )(x) =x }}$
