Answer
No.
Work Step by Step
The two functions are inverses of each other if $(f\circ g)(x)=(g \circ f)(x)$.
For the given functions,
$(f\circ g)(x)
\\=f(g(x))
\\=-3\times (-\frac{1}{3}x-12)+12
\\=x+36+12
\\=x+48$
Therefore, $f$ and $g$ are not inverses of each other..