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