Answer
$(-\infty,\ 2)\cup (2,\ \infty)$
Work Step by Step
We are given:
$f(x)= \frac{1}{3x-6}$
The domain of a function consists of all the values that $x$ is allowed to have. In this case, we can not have division by $0$:
$3x-6\ne 0$
$3x\ne6$
$x\ne2$
Thus the domain is: $(-\infty,\ 2)\cup (2,\ \infty)$
