Concept explainers
(a)
To explain: The definition of one-to-one function.
(a)
Explanation of Solution
A function f is called one-to-one if every element of the range corresponds to exactly one element of the domain.
That is, if
In other words, a function is said to be one to one if every image as a unique pre image in the domain.
Graph is one-to-one if and only if every horizontal line intersect function f at most once.
Therefore, horizontal line must cross at only one point or it should be parallel to the graph.
(b)
To define: The inverse function
(b)
Answer to Problem 12RCC
Solution:
If the function f is one-to-one then the graph of f and graph of
Explanation of Solution
Given:
Function f is a one-to-one function.
Let
Replace x by y
Take
Check whether the graph of the function f is one-to-one by the horizontal line test in order to find the graph of
If the function f is not one-to-one then
If the function f is one-to-one then the graph of f and graph of
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