Answer
The pair of provided functions $f\left( x \right)=\sqrt{2.5x+9.25}$ and $g\left( x \right)=0.4{{x}^{2}}-3.7,\text{ }x\ge 0$ are inverses of each other.
Work Step by Step
$f\left( x \right)=\sqrt{2.5x+9.25}$and$g\left( x \right)=0.4{{x}^{2}}-3.7,\text{ }x\ge 0$
Now apply the formula of composition of two functions
$f\circ g\left( x \right)=f\left( g\left( x \right) \right)$
Substitute $0.4{{x}^{2}}-3.7$ for$g\left( x \right)$ in the above equation
$f\circ g\left( x \right)=f\left( 0.4{{x}^{2}}-3.7 \right)$
Substitute $0.4{{x}^{2}}-3.7$ for $x$ in the provided function $f\left( x \right)$; the above equation becomes
$f\circ g\left( x \right)=\sqrt{2.5\left( 0.4{{x}^{2}}-3.7 \right)+9.25}$
Use the distributive property in the above equation:
$\begin{align}
& f\circ g\left( x \right)=\sqrt{2.5\times 0.4{{x}^{2}}-2.5\times 3.7+9.25} \\
& =\sqrt{{{x}^{2}}-9.25+9.25} \\
& =\sqrt{{{x}^{2}}} \\
& =x
\end{align}$
Here, the composition of two functions is the identity function.
