# What is the domain of the function f(x)=(x+1)/(2x-1)?

Aug 9, 2014

With these sorts of functions the value of $x$ that makes the bottom part of the fraction equal zero is a vertical asymptote .

So in this example $f \left(x\right) = \frac{x + 1}{2 x - 1}$
$2 x - 1 = 0$
$2 x = 1$
$x = \frac{1}{2}$

Therefore $f \left(x\right)$ is defined for every value of $x$ except for $x = \frac{1}{2}$

Therefore the domain is $x \in$[$- \infty$,$\frac{1}{2}$ )$\cup$ ($\frac{1}{2}$,$\infty$]