Concept explainers
(a)
To find: The function
(a)
Answer to Problem 30E
The sum of the functions
Explanation of Solution
Given:
The functions are
Result used:
The sum of the functions
Calculation:
Substitute the value of
As the radicand cannot take negative values,
On simplification,
Also
Simplify the above inequality as follows.
So the value of x lies in the interval
Hence, the domain of
So the combined domain is
Therefore, the domain of
(b)
To find: The function
(b)
Answer to Problem 30E
The function
Explanation of Solution
Result used:
The function
Calculation:
Substitute the value of
From part (a), the domain of the function
Therefore, the value of the given function is
(c)
To find: The function
(c)
Answer to Problem 30E
The product function
Explanation of Solution
Result used:
The product function
Calculation:
Substitute the value of
From part (a), the domain of the function
Therefore, the value of the given function is
(d)
To find: The function
(d)
Answer to Problem 30E
The quotient function is
Explanation of Solution
Result used:
The quotient function
Calculation:
Substitute the value of
Thus, the quotient function is defined when the denominator is not equal to 0.
Hence, the function is
Simplify the equation
So, the numbers −1 and 1 are excluded from the domain.
From part (a), the domain of the function
Remove −1 and 1 from
Therefore, the domain of the function is
Therefore, the value of the given function is
Chapter 1 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning