Answer
$y=f[g(x)],$
$f(x)=x^{1/3}-2x^{2/3}+7,\qquad g(x)=x^{2}+5x$
Work Step by Step
A reliable method is asking:
"How would we calculate this on a calculator?".
First, calculate $g(x)=x^{2}+5x$
and then, calculate: $\quad [g(x)]^{1/3}- 2 [g(x)]^{2/3}+7$
(apply $f(x)=x^{1/3}-2x^{2/3}+7\quad $ on g(x) instead of x)
$f[g(x)]= [g(x)]^{1/3}- 2[g(x)]^{2/3}+7$
$=(x^{2}+5x)^{1/3}-2(x^{2}+5x)^{2/3}+7$
$=y$