What is the domain of the function $f (x) = \frac{x + 1}{2 x - 1}$ $f(x)=(x+1)/(2x-1)$ ?

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Answer 1 · 2014-08-09T13:22:42

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

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

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

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

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