Answer
$f(g(x))=x$ and $g(f(x))=x$
Work Step by Step
$f(x)=\frac{2}{x-5}, g(x)=\frac{2}{x}+5=\frac{2+5x}{x}$
$f(g(x))=\frac{2}{\frac{2+5x}{x}-5}=\frac{2x}{2}=x$
and
$g(f(x))=\frac{2+5\left(\frac{2}{x-5}\right)}{\frac{2}{x-5}}=\frac{2x}{2}=x$.
$f(g(x))= g(f(x))= x.$
Thus, $f(x)$ and $g(x)$ are Inverse of each other.
