Answer
Domain:
$(-\infty, \frac{1}{2}) \cup (\frac{1}{2}, +\infty)$
Work Step by Step
The given rational function is defined for real numbers $x$ except the x-value that will make the denominator equal to zero.
To find the number that will make the denominator equal to 0, equate the denominator to zero, then solve the equation to obtain:
$2x-1 = 0
\\2x=1
\\x=\frac{1}{2}$
Thus, the domain of $f$ is the set of real numbers except $\frac{1}{2}$.
In interval notation, the domain is $(-\infty, \frac{1}{2}) \cup (\frac{1}{2}, +\infty)$.
