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Concept explainers
For the unction
Graph
Determine the inverse of
On the same coordinate axes as
(a)
![Check Mark](/static/check-mark.png)
The domain, range and horizontal asymptote of the graph of
Answer to Problem 11CR
Solution:
Domain of
Range of
Horizontal asymptote is
Graph is:
Explanation of Solution
Given information:
The function
Explanation:
The parent function for the transformation is
The exponential function
Since
Therefore, the graph of function
The transformation
To get the graph of
Therefore, the graph of function
Domain of the function is set of all
From graph function,
In an interval notation, the domain of function
Range of function is the set of all
From graph, it is clear that the range of function is the set of all
In an interval notation, the range of function
The line
(b)
![Check Mark](/static/check-mark.png)
The inverse of
Answer to Problem 11CR
Solution:
The inverse function of
Domain of function
Range of function
Vertical asymptote is line
Explanation of Solution
Given information:
The function
Explanation:
Let
In function
Solve this equation for
Subtract
This can also be written as
Apply logarithm to the base
Apply power rule of logarithm
Apply logarithmic rule
The inverse function is
To check
To check
Using power rule of logarithm,
Since
To check
Apply the rule
So,
Therefore, the inverse function of
Range of function
Since the range of function
Domain of function
Since the domain of function
For logarithmic function
The graph of function
Vertical asymptote of function
Therefore, the vertical asymptote of function
(c)
![Check Mark](/static/check-mark.png)
To graph: The functions
Explanation of Solution
Given information:
The functions
Explanation:
The graphs of functions
So, the graphs of functions
The function
The function
Therefore, the graph of
Interpretation:
The graph represents the functions
Chapter 5 Solutions
Precalculus
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus & Its Applications (14th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
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