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Q. 1

Expert-verified

Precalculus Enhanced with Graphing Utilities

Found in: Page 395

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

The domain of the function $f (x) = \frac{x + 1}{2 x + 1}$ is _______.

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

We have:

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

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:

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

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

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

Set builder form: $\{x | x \neq - \frac{1}{2}\}$

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