Concept explainers
To find: The condition for the slope of a linear function to be one-to-one. To find the inverse of a linear one-to-one function and its slope.
Answer to Problem 90E
A linear function
The inverse of the given
Yes, the inverse of the given function linear.
The slope of the inverse function is
Explanation of Solution
Given information: A linear function
Concept used:
The linear function can be written as
A function with domain A is called a one-to one function if no two elements of A have the same image, that is
To be one-to-one the function should not have any repeated value horizontally.
If
Calculation:
The linear function is
To be one-to-one the function should not have any repeated value horizontally.
Since, the given function is linear; to be one-to-one it should not be a line parallel to X-axis.
The slope of a line parallel to x-axis is
So, to be a one-to-one function the slope have to be not equal to
Let,
Therefore, the inverse of the given
Yes, the inverse of the given function linear as it can be written in the form of
The slope of the inverse function is
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