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 $\bf{g}$
$\bf{f(x) = 4x+2 }$ and $\bf{g(x) = \dfrac{1}{4}(x-2) }$
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) $
$ 4(\dfrac{1}{4}(x-2))+2 = \dfrac{1}{4}(4x+2-2) $
$ \dfrac{4}{4}(x-2)+2 = \dfrac{4}{4}x+\dfrac{2}{4}-\dfrac{2}{4} $
$ 1(x-2)+2 = 1x $
$ x-2+2 = x $
$x=x$
Thus we see that, $\color{blue}{\bf{ ( f \text{ }\omicron\text{ g} )(x) = ( g \text{ }\omicron\text{ f} )(x) =x }}$
