Concept explainers
In Problems 12-14, find for each pair of functions. State the domain of each of these functions.
To find: The pair of function from the provided functions.
Answer to Problem 12RE
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 quadratic equation is any equation/function with a degree of 2 that can be written in the form , where and are real numbers, and a does not equal to 0. Its graph is called a parabola. The constants , and are called the parameters of the equation. The values of and determine the shape and position of the parabola.
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 defined 2 multiplied by and added 1 with it. The input of the function takes all the real values in the real line. Therefore, the domain of the pair is the set of all real numbers.
b. For , . Here the function is defined multiplied by and added 1 with it. The input of the function takes all the real values in the real line. Therefore, the domain of the pair is the set of all real numbers.
c. 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.
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 . The domain of the pair is .
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Precalculus (10th Edition)
Calculus: Early Transcendentals (3rd Edition)
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