Answer
$f(g(x))=x$ and $g(f(x))=x$ so $f$ and $g$ are inverses of each other.
There are no restrictions to their domains.
Work Step by Step
Substitute $g(x)$ to $x$ in $ f(x)$ to obtain:
\begin{align*}
f\left(g(x)\right)&=3\left(\frac{1}{3}(x-4)\right)+4\\
&=1(x-4)+4\\
&=x-4+4\\
&=x
\end{align*}
Substitute $f(x)$ to $x$ in $g(x)$ to obtain:
\begin{align*}
g\left(f(x)\right)&=\frac{1}{3}\left(3x+4-4\right)\\
&=\frac{1}{3}(3x)\\
&=x
\end{align*}
Since $f(g(x))=g(f(x))=x$, then $f$ and $g$ are inverses of each other.
Both $f(x)$ and $g(x)$ have the set of real numbers as a domain so the inverse has no restrictions.