# How do you find the domain of this function f(x)=1/(3x-6)?

Apr 25, 2015

The only value of $x$ for which $f \left(x\right) = \frac{1}{3 x - 6}$ is not defined is $x = 2$ (since this would result in division by zero).

The Domain of $f \left(x\right)$ is
$\left(- \infty , 2\right) \cup \left(2 , + \infty\right)$

Apr 25, 2015

Domain $\left(- \infty , 2\right) U \left(2 , \infty\right)$

To find the domain of a function, we first identify the values of x for which f(x) becomes undefined. In the present case, it is observed that if x=2, then f(x) becomes $\frac{1}{0}$ or $\infty$. Hence the domain would be all real numbers except 2. In interval notation it can be expressed as $\left(- \infty , 2\right) U \left(2 , \infty\right)$. In the set builder notation it would be written as {x:$\in R$ | x$\notin$2}