Answer
Since $f\circ g(x)=x$ and $g\circ f(x)=x $
f and g are inverses of each other.
Work Step by Step
$\begin{array}{lllll}
f\circ g(x) & =f[g(x)] & ..... & g\circ f(x) & =g[f(x)]\\
& =\sqrt{4-[g(x)]^{2}} & & & =\sqrt{4-[f(x)]^{2}}\\
& =\sqrt{4-[(4-x^{2})^{1/2}]^{2}} & & & =\sqrt{4-[(4-x^{2})^{1/2}]^{2}}\\
& =\sqrt{4-(4-x^{2})} & & & =\sqrt{4-(4-x^{2})}\\
& =\sqrt{x^{2}} & & & =\sqrt{x^{2}}\\
& =x, 0\leq x\leq 2 & & & =x, 0\leq x\leq 2
\end{array}$
Since $f\circ g(x)=x$ and $g\circ f(x)=x $
f and g are inverses of each other.