Answer
$\{x\in R: x \neq 2\}=(-\infty , 2) \cup (2, \infty)$
Work Step by Step
The domain of $f(x)=\frac{1}{3x-6}$ is the set of all real numbers $x$ for which $\frac{1}{3x-6}$ is defined as a real number. We know a rational expression is not defined where the denominator is zero, so we must find all values of $x$ for which $$3x-6 =0.$$ We add $6$ to both sides to get $$3x=6,$$ and dividing both sides by $3$ gives $$x=2.$$ Thus we know $\frac{1}{3x-6}$ is not defined when $x=2$. This means the domain of $f(x)=\frac{1}{3x-6}$ is the set af all real numbers $x$ for which $x\neq 2$
In set notation, the domain is $\{x\in R: x \neq 2\}.$
In interval notation, the domain is $(-\infty , 2) \cup (2, \infty).$