Answer
$\color{blue}{\bf{ f(x)= \sqrt{x} \text{ ; } g(x)= x^2-1 }}$
$\color{blue}{\bf{\text{or other equivalent functions}}}$
Work Step by Step
We are given the function $\bf{h(x)= \sqrt{x^2-1} }$ and are asked to find two functions ${f(x)}$ and ${g(x)}$ such that $( f \text{ }\omicron\text{ g} )(x) =h(x)$
There are many ways to do this, for example:
$\color{magenta}{f(x)= \sqrt{x} }$ and $\color{lime}{g(x)= x^2-1 }$
$\color{magenta}{ \sqrt{ \color{lime}{ x^2-1 } } }$
$\color{blue}{\bf{ f(x)= \sqrt{x} \text{ ; } g(x)= x^2-1 }}$
$\color{blue}{\bf{\text{or other equivalent functions}}}$