Answer
Proved below.
Work Step by Step
$f\left( x \right)\,\,\text{and}\,\,g\left( x \right)$
Evaluate the function $\left( \left( f\circ g \right)\circ h \right)\left( x \right)$ as follows.
$\left( \left( f\circ g \right)\circ h \right)\left( x \right)=\left( f\circ g \right)\left( h\left( x \right) \right)$
Apply the definition of composition functions.
$\left( \left( f\circ g \right)\circ h \right)\left( x \right)=\left( f\left( g\left( h\left( x \right) \right) \right) \right)$
Use the fact $g\left( h\left( x \right) \right)=\left( g\circ h \right)\left( x \right)$,
$\begin{align}
& \left( \left( f\circ g \right)\circ h \right)\left( x \right)=f\left( \left( g\circ h \right)\left( x \right) \right) \\
& =\left( f\circ \left( g\circ h \right) \right)\left( x \right)
\end{align}$
Hence, it is proved that $\left( \left( f\circ g \right)\circ h \right)\left( x \right)=\left( f\circ \left( g\circ h \right) \right)\left( x \right)$.
