Single Variable Calculus, Chapter 1, 1.1, Section 1.1, Problem 27

Determine the domain of the function $\displaystyle f(x) = \frac{x}{3x - 1}$




The function given is a rational function that is defined for every numbers except for the values of $x$ that could make the denominator equal to 0.



$
\begin{equation}
\begin{aligned}
3x - 1 &= 0\\
3x & = 1\\
x & = \frac{1}{3}
\end{aligned}
\end{equation}
$


Therefore,
The domain of the function is: $\displaystyle \left(-\infty, \frac{1}{3}\right)\bigcup \left(\frac{1}{3}, \infty\right)$