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Concept explainers
(a)
To draw: Thegraph of
(a)
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Explanation of Solution
Given information:The given functions are
Graph:
To draw the graph of
Step 1: Press “ON” button on graphical calculator and press
Step 2: Enter the keystrokes
Step 3: Turn off
Step 4: Now, to write the equation
Step 5: Set the window at the interval
Figure (1)
Interpretation: From the graph it can be observed that the domain of the function
(b)
To find: The domain of
(b)
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Answer to Problem 71E
The domain of
Explanation of Solution
Given information:The given functions are
Calculation:
The domain of a function is the set of all
The function
The function
From part (a), the domain of the function
Therefore, the domain of
(c)
To find: The domains of functions
(c)
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Answer to Problem 71E
The domain of the functions
Explanation of Solution
Given information:The given functions are
Calculation:
To draw the graph of
To write the equation
Now, set the window at the interval
Figure (2)
To draw the graph of
To write the equation
Now, set the window at the interval
Figure (3)
To write the equation
Now, set the window at the interval
Figure (4)
To write the equation
Now, set the window at the interval
Figure (5)
To write the equation
Now, set the window at the interval
Figure (6)
Therefore, from the graph above graphs it can be interpreted that the domain of the functions
(d)
To find: The conjecture that can be made about the domain of sums, difference, products and quotients of functions.
(d)
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Answer to Problem 71E
The domain of sum, difference and products of two functions is the intersection of the domains of given functions.The domain of quotient of functions is the intersection of their domains by removal of any zeros of the denominators.
Explanation of Solution
Given information:The given functions are
The domain of the function
From part (a), the domain of the function
From part (b), the domain of the functions
From part (a) and part (b), it can be observed that the domain of sum, difference and products of two functions is the intersection of the domains of given functions.
The domain of quotient of functions is the intersection of their domains by removal of any zeros of the denominators.
Chapter 1 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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