Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 5.4, Problem 22WE

a.

To determine

To find the domain of the given rational function.

a.

Expert Solution
Check Mark

Answer to Problem 22WE

Domain: (−∞,−2)∪(−2,2)∪(2,∞)

Explanation of Solution

Given:

Rational function: g(x)=x3+2xx2−4

Concept used:

To find the domain of the rational function, the following steps are to be followed:

  1. Equate the denominator equal to zero.
  2. Solve and find the x values that make the denominator equal to zero.
  3. The domain is all the real numbers except for those x values equal to zero.

Calculation:

The given rational function is g(x)=x3+2xx2−4

The denominator of the given function is x2−4.

Equating the denominator to zero,

  ⇒x2−4=0

Adding 4 on both sides,

  ⇒x2−4+4=0+4⇒x2=4

Taking square root on both sides,

  ⇒x2=4⇒x=± 2

Hence, the domain of the function is all real numbers except x=± 2.

Conclusion:

Therefore, the domain of the function is a (−∞,−2)∪(−2,2)∪(2,∞).

b.

To determine

To find the zeros of the function if any.

b.

Expert Solution
Check Mark

Answer to Problem 22WE

  x=±2i

Explanation of Solution

Given:

Rational function: g(x)=x3+2xx2−4

Concept used:

To find the zeros of the rational function,

  1. Equate g(x)=0.
  2. Simplify and find the values of x which are the zeros of the rational function.

Calculation:

Equate the rational function g(x) to zero.

  ⇒g(x)=0⇒x3+2xx2−4=0

Cross multiplying,

  ⇒x3+2x=(x2−4)(0)⇒x3+2x=0⇒x(x2+2)=0⇒x=0 and x2+2=0⇒x=0 and ⇒x2+2=0

Subtracting 2 on both sides,

  ⇒x2+2−2=0−2⇒x2=−2

Taking square root on both sides,

  ⇒x2=−2⇒x=±2i

Conclusion:

Therefore, the zeroes of the rational function are x=±2i .

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Chapter 5.4, Problem 21WE
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Chapter 5.4, Problem 23WE

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 1OECh. 5.1 - Prob. 2OECh. 5.1 - Prob. 3OECh. 5.1 - Prob. 4OECh. 5.1 - Prob. 5OECh. 5.1 - Prob. 6OECh. 5.1 - Prob. 7OECh. 5.1 - Prob. 8OECh. 5.1 - Prob. 9OECh. 5.1 - Prob. 10OE
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