
Concept explainers
(a)
The domain of
(a)

Answer to Problem 12CT
Solution:
The domain of the function
Explanation of Solution
Given information:
The function is
Explanation:
Consider the function
The given function can be written as
The given function is exponential function.
The domain of the exponential function is
Thus, the domain of the function
(b)
To graph: The function
(b)

Explanation of Solution
Given information:
The function is
Graph:
Use the steps below to graph the function using graphing calculator:
Step I: Press the ON key.
Step II: Now, press [Y=]. Input the right hand side of the function
Step III: Then hit [Graph] key to view the graph.
The graph of the function
Interpretation:
By looking at the graph, it is observed that as
(c)
The range of any asymptotes from the graph of
(c)

Answer to Problem 12CT
Solution:
1) The range of the function
2) The horizontal asymptote of
Explanation of Solution
Given information:
The function is
Explanation:
The domain of the function
Range of the function is the set of values of the dependent variable for which a function is defined.
From the graph, range of
As
Therefore, the horizontal asymptote of
(d)
The inverse of
(d)

Answer to Problem 12CT
Solution:
The inverse of
Explanation of Solution
Given information:
The function is
Explanation:
Consider the function
Step 1: Replace
Step 2: Interchange the variables
Interchange the variables
Step 3: Solve for
Add
Taking natural logarithm function from both sides of
By using
By using
Replace
Therefore, the inverse of
(e)
The domain and range of
(e)

Answer to Problem 12CT
Solution:
The domain of
Explanation of Solution
Given information:
The function is
Explanation:
From the part (d),
The logarithm function is defined only for positive real numbers.
The domain of the function is the set of real numbers such that
The domain of
The domain of the function
By using domain of
The range of
Therefore, the domain of
(e)
To graph: The function
(e)

Explanation of Solution
Given information:
The function is
Graph:
From the part (d),
Use the steps below to graph the function using graphing calculator:
Step I: Press the ON key.
Step II: Now, press [Y=]. Input the right hand side of the function
Step III: Then hit [Graph] key to view the graph.
By using the graphing calculator, the graph of the function
Interpretation:
By looking at the graph, it is observed that as
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