Concept explainers
To find: A formula and domain for inverse function and interpret the meaning of inverse function.
Answer to Problem 19E
The inverse function is,
The domain of the inverse function is
Explanation of Solution
Given:
The Celsius temperature as a function of the Fahrenheit temperature is
Calculation:
Solve the Celsius temperature function for F.
Thus, the inverse function is,
It is known that the range of a function is the domain of its inverse function.
So, first find the range of the given function.
Since the function is defined when
Substitute the end points of domain for F in the given function and find its range as follows.
Thus, the range of the given function is,
Therefore, the domain of the inverse 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