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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 4: Q. 18 (page 225)

Find the domain of the rational function.
$Q (x) = \frac{- x (1 - x)}{3 x^{2} + 5 x - 2}$

Short Answer

Expert verified

The domain of the given function is

(- 鈭� 鈥�, 鈥� - 2) 鈭� (- 2, 鈥� \frac{1}{3}) 鈭� (\frac{1}{3}, 鈥� 鈭� 鈥�)

Step by step solution

01

Step 1. Given information

The given function is $Q (x) = \frac{- x (1 - x)}{3 x^{2} + 5 x - 2}$

02

Step 2. Find the domain

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

So,

$3 x^{2} + 5 x - 2 鈮� 0 3 x^{2} + 6 x - x - 2 鈮� 0 3 x (x + 2) - (x + 2) 鈮� 0 [t a k i n g o u t 3 x a n d - 1 a s c o m m o n] (3 x - 1) (x + 2) 鈮� 0 [t a k i n g o u t x + 2 a s c o m m o n] 3 x - 1 鈮� 0 3 x 鈮� 1 x 鈮� \frac{1}{3} o r x + 2 鈮� 0 x 鈮� - 2$

Thus, the domain of the given function is all real numbers except $- 2$ and $\frac{1}{3}$ .

Therefore, the domain is $(- 鈭� 鈥�, 鈥� - 2) 鈭� (- 2, 鈥� \frac{1}{3}) 鈭� (\frac{1}{3}, 鈥� 鈭� 鈥�)$

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Most popular questions from this chapter

Find the domain of the rational function.

$R (x) = \frac{4 x}{x - 3}$

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.

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

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In Problems $7 - 44$ , follow Steps $1$ through 7 on page $228$ to analyze the graph of each function.

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