Answer
$(f\circ g)(x)=\sqrt{x^2-2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the value of the given expression, $
\left( f\circ g \right)(x)
,$ given that
\begin{array}{l}\require{cancel}
f(x)=\sqrt{x-2}
\\g(x)=x^2
,\end{array}
use the definition of function composition.
$\bf{\text{Solution Details:}}$
Using $(f\circ g)(x)=f(g(x)),$ then
\begin{array}{l}\require{cancel}
(f\circ g)(x)=f(g(x))
.\end{array}
Since $
g(x)=x^2
,$ the equation above becomes
\begin{array}{l}\require{cancel}
(f\circ g)(x)=f(x^2)
.\end{array}
Substituting $x$ with $x^2$ in $f,$ the equation above becomes
\begin{array}{l}\require{cancel}
(f\circ g)(x)=\sqrt{x^2-2}
.\end{array}