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Concept explainers
To find: The pair of function from the provided functions.
![Check Mark](/static/check-mark.png)
Answer to Problem 13RE
Solution:
a. The domain of the pair is the set of all real numbers.
b. The domain of the pair is the set of all real numbers.
c. The domain of the pair is the set of all real numbers.
d. The domain of the pair is .
Explanation of Solution
Given:
It is provided in the problem that the function and .
Formula used:
A
The domain of a function is the set of all real values of that will give real values for . The range of a function is the set of all real values of that you can get by plugging real numbers into .
Calculation:
a. For , . Here the function is a quadratic equation. By the definition of domain of the quadratic equation, the domain takes all the real values. Therefore, the domain of the pair is the set of all real numbers.
b. For , . Here the function is a quadratic equation. By the definition of domain of the quadratic equation, the domain takes all the real values. Therefore, the domain of the pair is the set of all real numbers.
c. For , . Here the function is an algebraic equation of degree 3. Therefore, there will not be any restriction for this equation. The input takes all the real values. Therefore, the domain of the pair is the set of all real numbers.
d. For , . The function says to divide by . Since division by 0 is not defined, the denominator can never be 0, so can never equal 0. The domain of the pair is .
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
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