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Concept explainers
(a)
The domain and the range of the function
(a)
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Answer to Problem 4CR
Solution:
The domain of the function
Explanation of Solution
Given information:
The function
Explanation:
The domain of
The function
The domain of the exponential function is the set of all real numbers
Therefore, the domain of the given exponential function is
The range of a function is the set of dependent variables for which the function is defined.
The range of exponential function is all real numbers greater than zero.
Then the range of
For all values of
Then,
Hence, the range of
(b)
The inverse of
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 4CR
Solution:
The inverse of
Explanation of Solution
Given information:
The function
Explanation:
To find the inverse function
Now, solve
Applying logarithm on both sides
The inverse function of
The domain of
The function
The logarithm function is valid on the positive real axis.
The domain of the logarithmic function is all real numbers greater than zero, such as
Then,
Therefore, the domain of the given function
The range of a function is the set of dependent variables for which the function is defined.
The range of the logarithmic function is all real numbers, which is
Hence, the range of
Chapter 10 Solutions
Precalculus
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Precalculus
University Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
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