Chapter 7: Q. 372 (page 732)

Solve each rational function inequality and write the solution in interval notation.
Given the function $R (x) = \frac{(x + 1)}{(x + 3)}$ , find the values of x that make the function less than or equal to 0.

Short Answer

Expert verified

Solution for inequality is $x \in (- 3, - 1] .$

Step by step solution

Step 1. Given Information

Given that the function is $R (x) = \frac{(x + 1)}{(x + 3)} \leq 0 .$

Step 2. Critical point

To find the critical point,

$(x + 1) = 0 x = - 1 (x + 3) = 0 x = - 3 At x = - 1, R (x) = \frac{0}{2} = 0 At x = - 3, R (x) = \frac{- 2}{- 0} = \infty$

The polynomial function which is undefined will not included in interval.

Step 3. Number line

It can be drawn as,

Step 4. Testing of polynomial expression

On testing the polynomial expression sign in every interval, it can be indicated.

$\frac{(x + 1)}{(x + 3)} \leq 0, (- 3, - 1] Thus, R (x) \leq 0 for x \in (- 3, - 1] .$

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.

Solve each rational function inequality and write the solution in interval notation.
Given the function $R (x) = \frac{(x + 1)}{(x + 3)}$ , find the values of x that make the function less than or equal to 0.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Critical point

Step 3. Number line

Step 4. Testing of polynomial expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve each rational function inequality and write the solution in interval notation.Given the functionR(x)=(x+1)(x+3), find the values of x that make the function less than or equal to 0.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Critical point

Step 3. Number line

Step 4. Testing of polynomial expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve each rational function inequality and write the solution in interval notation.
Given the function $R (x) = \frac{(x + 1)}{(x + 3)}$ , find the values of x that make the function less than or equal to 0.