Concept explainers
To state: that whether the function is one-to-one or not and verify graphically.
Answer to Problem 69E
Yes, the function is one-to-one and the inverse function is
Explanation of Solution
Given information : thefunction is,
let
Since
to graph the given function first create a table for plotting the points and then make a curve smoothly by jointing the points.
x | y |
-2 | 4 |
-3 | 5 |
-4 | 6 |
-5 | 7 |
The graph can be obtained as:
From the above graph, it can be observed that the graph of the function hasno horizontal lines that intercept the graph more than one times, so the function isa one-to-one and its inverse functionexists.
Now for inverse function, substitute
Thus, the inverse function is
Chapter 1 Solutions
EBK PRECALCULUS W/LIMITS:GRAPH.APPROACH
- 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