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
Write g(x) in exponential form, $g(x)=x^{1/5}.$
$\begin{array}{lllll}
f\circ g(x) & =f[g(x)] & ..... & g\circ f(x) & =g[f(x)]\\
& =[g(x)]^{5} & & & =[f(x)]^{1/5}\\
& =[x^{1/5}]^{5} & & & =[x^{5}]^{1/5}\\
& =x^{1} & & & =x^{1}\\
& =x & & & =x
\end{array}$
Since $f\circ g(x)=x$ and $g\circ f(x)=x$,
f and g are inverses of each other.