StudySmarter AI is coming soon!

:00Days
:00Hours
:00Mins
00Seconds

A new era for learning is coming soonSign up for free

Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q. 16

Expert-verified

Precalculus Enhanced with Graphing Utilities

Found in: Page 225

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Find the domain of the rational function.
$G (x) = \frac{6}{(x + 3) (4 - x)}$

The domain of the given function is $(- \infty, - 3) \cup (- 3, 4) \cup (4, \infty)$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

The given function is $G (x) = \frac{6}{(x + 3) (4 - x)}$

Step 2. Find the domain

For the domain, the denominator should not be equal to zero.

So,

$(x + 3) (4 - x) \neq 0 x + 3 \neq 0 x \neq - 3 o r 4 - x \neq 0 x \neq 4$

Thus, the domain of the given function is all real numbers except $- 3$ and $4$ .

Therefore, the domain is $(- \infty, - 3) \cup (- 3, 4) \cup (4, \infty)$

Most popular questions for Math Textbooks

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. $R (x) = \frac{6 x^{2} + 7 x - 5}{3 x + 5}$

In Problems 63–72, find the real solutions of each equation.

$x^{4} - x^{3} + 2 x^{2} - 4 x - 8 = 0$

Find the domain of the rational function.

$F (x) = \frac{3 x (x - 1)}{2 x^{2} - 5 x - 3}$

Solve the inequality $x^{2} - 5 x \leq 24$ . Graph the solution set.

Find the domain of the rational function.

$R (x) = \frac{x}{x^{3} - 8}$

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free