Concept explainers
We can express the functions in Exercise 3 algebraically as
f(x) = _____
g(x) = _____
(f ○ g)(x) = _____
(g ○ f)(x) = _____
3. If the rule of the function f is “add one” and the rule of the function g is “multiply by 2,” then the rule of f ○ g is “____________________”, and the rule of g ○ f is “____________________.”
To evaluate: The values of functions
Answer to Problem 4E
The values of function
Explanation of Solution
Section1:
The rule of the function f is adding one.
So, the value of function
Thus, the value of function
Section2:
The rule of the function f is multiply by 2.
So, the value of function
Thus, the value of function
Section3:
The rule of the function f is add one and the rule of the function g is multiply by 2.
From section 2:
The value of function
From section3:
The value of function
The function
Substitute the values of
Thus, the value of function
Section4:
The rule of the function f is add one and the rule of the function g is multiply by 2.
From section 2:
The value of function
From section3:
The value of function
The function
Substitute the values of
Thus, the value of function
Chapter 2 Solutions
Precalculus: Mathematics for Calculus - 6th 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