Chapter 6: Q. 1 (page 395)

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

Short Answer

Expert verified

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

Step by step solution

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the domain.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Geometry

Mechanics Maths

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

The domain of the functionf(x)=x+12x+1is _______.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the domain.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Geometry

Mechanics Maths

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

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