Answer
$f(g(x))=x$ and $g(f(x))=x$.
Work Step by Step
$f(x)=\frac{3}{x-4}, g(x)=\frac{3}{x}+4=\frac{3+4x}{x}$
$f(g(x))=\frac{3}{\frac{3+4x}{x}-4}=\frac{3x}{3}=x$ and $g(f(x))=\frac{3+4(\frac{3}{x-4})}{\frac{3}{x-4}}=\frac{3x}{3}=x$.
$f(g(x))= g(f(x))= x$.
Thus, $f(x)$ and $g(x)$ are Inverse of each other.
