Answer
$H(x)$ = $(f\circ g\circ h)(x)$ for
$h(x)=|x|,$
$g(x)=2+x$, and
$f(x)=\sqrt[8]{x}$
Work Step by Step
$(f\circ g\circ h) (x)=f[g(h(x))]$
If we used a calculator, step by step,
for each step,
define the operation we would perform on the current result.
Starting with x, we would
1. calculate $|x|,\ \ \ h(x)=|x|$
2. add 2 to the current result, $\ \ g(x)=x+2$
3. if the current result was R, calculate $\sqrt[8]{R},\ \ \ f(x)=\sqrt[8]{x}$
$H(x)$ = $(f\circ g\circ h)(x)$ for
$h(x)=|x|,$
$g(x)=2+x$, and
$f(x)=\sqrt[8]{x}$
