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 21WE

To determine

To find the domain of the given rational function.

Expert Solution

Answer to Problem 21WE

Domain: (−∞,0)∪(0,9)∪(9,∞)

Explanation of Solution

Given:

Rational function: f(t)=t2−9t2−9t

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 t values that make the denominator equal to zero.
The domain is all the real numbers except for those t values equal to zero.

Calculation:

The given rational function is f(t)=t2−9t2−9t

The denominator of the given function is t2−9t.

Equating the denominator to zero,

⇒t2−9t=0⇒t(t−9)=0

⇒t=0 and t−9=0

Therefore,

⇒t=0 and

⇒t−9=0

Adding 9 on both sides,

⇒t−9+9=0+9⇒t=9

Hence, the domain of the function is all real numbers except t=0 and t=9.

Conclusion:

Therefore, the domain of the function is a (−∞,0)∪(0,9)∪(9,∞).

To determine

To find the zeros of the function if any.

Expert Solution

Answer to Problem 21WE

t=3

Explanation of Solution

Given:

Rational function: f(t)=t2−9t2−9t

Concept used:

To find the zeros of the rational function,

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

Calculation:

Equate the rational function f(t) to zero.

⇒f(t)=0⇒t2−9t2−9t=0

Cross multiplying,

⇒t2−9=(t2−9t)(0)⇒t2−9=0

Adding9 on both sides,

⇒t2−9+9=0+9⇒t2=9

Taking square root on both sides,

⇒t2=9⇒t=3

Conclusion:

Therefore, the zeroes of the rational function are t=3 .

Chapter 5.4, Problem 20WE

Chapter 5.4, Problem 22WE

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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