Concept explainers
(a)
To explain:The convincing argument that
(a)
Answer to Problem 51E
By the definition of one-to-one function, the function
Explanation of Solution
Given information:The function is
It is known that a function is one-to-one on its domain if
For any
As it is known that
Therefore, by the definition of one-to-one function, the function
(b)
To find:The formula for the inverse of
(b)
Answer to Problem 51E
The inverse of
Explanation of Solution
Given information:The function is
Calculation:
Interchange the
Substitute
As the slope of
Therefore, the inverse of
(c)
To write:The conclusion about the graphs of the inverse of the functions if the graph of two functions are parallel line with non-zero slope.
(c)
Answer to Problem 51E
The graphs of the inverse will be parallel lines with non-zero slope.
Explanation of Solution
Given information:It is given that the graphs of two functions are parallel lines with non-zero slope.
If the original functions hasslope
Therefore, the graphs of the inverse will be parallel lines with non-zero slope.
(d)
To write:The conclusion about the graphs of the inverse of the functions.
(d)
Answer to Problem 51E
The graphs of the inverse will be perpendicular lines with non-zero slope.
Explanation of Solution
Given information:It is given that the graphs of two functions are perpendicular lines with non-zero slope.
The lines are perpendicular so the original function will have the slopes
Since each of
Therefore, the graphs of the inverse will be perpendicular lines with non-zero slope.
Chapter 1 Solutions
Calculus: Graphical, Numerical, Algebraic
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