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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