Answer
The two functions f and g such that $\left( f\circ g \right)=\left( g\circ f \right)$ are $f\left( x \right)=x,g\left( x \right)=\frac{1}{x}$.
Work Step by Step
Let $f\left( x \right)=x,\text{ }g\left( x \right)=\frac{1}{x}$
The value of $\left( f\circ g \right)$ and $\left( g\circ f \right)$ can be calculated as below:
$\begin{align}
& f\left( g\left( x \right) \right)=g\left( x \right) \\
& =\frac{1}{x}
\end{align}$
$\begin{align}
& g\left( f\left( x \right) \right)=\frac{1}{f\left( x \right)} \\
& =\frac{1}{x}
\end{align}$
Hence, $f\left( g\left( x \right) \right)=g\left( f\left( x \right) \right)$
Hence, one of the possible pair of functions is $f\left( x \right)=x,\,\,g\left( x \right)=\frac{1}{x}$.
