Consider the functions $f(x) = e^{3 x}$, $g(x) = \ln(3\,x)$, $h(x) = \frac{\ln(x)}{3}$, $p(x) = \ln(x) - 3$, $q(x) = \ln(x) + 3$, $r(x) = 3\ln(x)$, and $s(x) = \ln\left(\frac{x}{3}\right)$.
Which of the following functions is an inverse function of $f(x)$?

A. $g(x)$
B. $h(x)$
C. $p(x)$
D. $q(x)$
E. $r(x)$
F. $s(x)$
G. None of these functions is an inverse function of $f(x)$.