
Concept explainers
a.
To Determine:
The inverse function of
To State:
What can the inverse function be used for.
The inverse function is
The inverse function can be used to find the corresponding percentage score if the GPA
Given:
The function
GPA is considered zero if percentage score is below
Concepts Used:
The inverse of
Isolating a variable from an equation.
Calculations:
Isolate the variable
The equation
Conclusion:
The inverse function is
The inverse function can be used to find the corresponding percentage score if the GPA
b.
To Determine:
If the domain of the inverse function has any restrictions.
Given:
The function
GPA is considered zero if percentage score is below
Known from previous part:
The inverse function is
Concepts Used:
Non integral exponents are not defined over negative bases.
The domain of a function limits the range of its inverse.
Calculations:
The inverse function
Thus, the input
Also since the domain of the original function
Conclusion:
The domain of the inverse function
c.
To Verify Graphically:
The function found in part a. is indeed the inverse of the given function
Given:
The function
GPA is considered zero if percentage score is below
Known from previous part:
The inverse function is
Concepts Used:
Graphing a function using a graphing calculator.
The graph of the inverse of a function is the original graph reflected about the line
Graphs:
The graph of the inverse function obtained algebraically is shown in red in the above figure.
The graph of inverse obtained by reflecting the original function’s graph about the line
Conclusion:
The graphs of the inverse function obtained using the two methods are found to be identical. Thus the algebraically found inverse function
Chapter 1 Solutions
EBK PRECALCULUS:GRAPHICAL,...-NASTA ED.
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