Answer
$f(g(x))=g(f(x))=x$. This means that $f(x)$ and $g(x)$ are inverses of each other.
Both $f(x)$ and $g(x)$ are continuous on the set of real numbers, so there are no restrictions to their domains.
Work Step by Step
We wish to plug $f(x)$ into $g(x)$ to obtain:
$$\displaystyle g[f(x)]=\frac{1}{3} (3x+4-4) \\=\dfrac{1}{3}(3x)\\=x$$
We wish to plug $g(x)$ into $f(x)$ to obtain:
$$f[(g(x)]=3(\dfrac{1}{3}(x-4))+4\\=1(x-4)+4\\=x-4+4\\=x$$
We see that $f(g(x))=g(f(x))=x$. This means that $f(x)$ and $g(x)$ are inverses of each other.
Both $f(x)$ and $g(x)$ are continuous on the set of real numbers, so there are no restrictions to their domains.