Answer
$ y $ is continuous in the domain
$$ R-\{2\}$$
Work Step by Step
Given $$ y=\frac{1}{x-2}-3 x $$
Find the zeros of the denominator:
$ x-2=0 \Rightarrow x=2$
So, $ y $ is continuous in the domain
$ R-\{2\}$
(all values except 2).