Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 5.4, Problem 13OE

To determine

To find the domain of the given rational function.

Expert Solution

Answer to Problem 13OE

Domain: (−∞,−1)∪(−1,1)∪(1,∞).

Explanation of Solution

Given:

Rational function: f(x)=x2+1x2−1

Concept used:

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

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

Calculation:

The given rational function is f(x)=x2+1x2−1

The denominator of the given function is x2−1.

Equating the denominator to zero,

⇒x2−1=0

Adding 1 on both sides,

⇒x2−1+1=0+1⇒x2=1

Taking square root on both sides,

⇒x2=1⇒x=±1

Hence, the domain of the function is all real numbers except x=±1.

Conclusion:

Therefore, the domain of the function is a (−∞,−1)∪(−1,1)∪(1,∞).

To determine

To find the zeros of the function if any.

Expert Solution

Answer to Problem 13OE

x=± i

Explanation of Solution

Given:

Rational function: f(x)=x2+1x2−1

Concept used:

To find the zeros of the rational function,

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

Calculation:

Equate the rational function f(x) to zero.

⇒f(x)=0⇒x2+1x2−1=0

Cross multiplying,

⇒x2+1=(x2−1)(0)⇒x2+1=0

Subtracting 1 on both sides,

⇒x2+1−1=0−1⇒x2=−1

Taking square root on both sides,

⇒x2=−1⇒x=± i

Conclusion:

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

Chapter 5.4, Problem 12OE

Chapter 5.4, Problem 14OE

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

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

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