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