Answer
Since $f\circ g(x)=x$ and $ g\circ f(x)=x \quad$ on their respective domains,
f and g are inverses of each other.
Work Step by Step
Write g(x) in exponential form, $g(x)=(x+9)^{1/2}$
$\begin{array}{lllll}
f\circ g(x) & =f[g(x)] & ..... & g\circ f(x) & =g[f(x)]\\
& =[g(x)]^{2}-9 & & & =[f(x)-9]^{1/2}\\
& =[(x+9)^{1/2}]^{2}-9 & & & =[x^{2-9+9}]^{1/2}\\
& =(x+9)-9 & & & =(x^{2})^{1/2}\\
& =x & & & =x
\end{array}$
Since $f\circ g(x)=x$ and $ g\circ f(x)=x \quad$ on their respective domains,
f and g are inverses of each other.