Answer
The statement is true.
Work Step by Step
Find the value of $\left( f\circ g \right)\left( 5 \right)$ as shown below:
$\begin{align}
& f\left( g\left( x \right) \right)=\sqrt{g\left( x \right)} \\
& =\sqrt{2x-1}
\end{align}$.
$\begin{align}
& f\left( g\left( 5 \right) \right)=\sqrt{5\cdot 2-1} \\
& =\sqrt{10-1} \\
& =\sqrt{9} \\
& =3
\end{align}$.
$\begin{align}
& g\left( 2 \right)=2\cdot 2-1 \\
& =4-1 \\
& =3
\end{align}$
Thus
$f\left( g\left( 5 \right) \right)=g\left( 2 \right)$
Hence, the statement is true.
