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Expert-verified Found in: Page 395 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # The domain of the function $f\left(x\right)=\frac{x+1}{2x+1}$ is _______.

The domain of the function $f\left(x\right)=\frac{x+1}{2x+1}$ is $\left\{x|x\ne -\frac{1}{2}\right\}$.

See the step by step solution

## Step 1. Given information.

We have:

$f\left(x\right)=\frac{x+1}{2x+1}$

## Step 2. Find the domain.

The domain of the function is the set of input values for which the function is real and defined.

Find the undefined points by comparing the denominator to zero:

$2x+1=0\phantom{\rule{0ex}{0ex}}2x=-1\phantom{\rule{0ex}{0ex}}x=-\frac{1}{2}$

The function domain is $x<-\frac{1}{2}\mathrm{or} x>-\frac{1}{2}$.

Interval notation: $\left(-\infty , -\frac{1}{2}\right)\cup \left(-\frac{1}{2}, \infty \right)$

Set builder form: $\left\{x|x\ne -\frac{1}{2}\right\}$ ### Want to see more solutions like these? 