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Chapter 8: Problem 73

How can a graphing utility be used to visually determine if two functions are inverses of each other?

Short Answer

Expert verified
A graphing utility can visually determine if two functions are inverses of each other by checking if their graphs are mirrored about the line \(y=x\). If the two graphs are reflections of one another across the line \(y=x\), then the two functions are inverses of each other.

Step by step solution

01

Plot the two functions

Given two functions, use the graphing utility to plot both functions on the same graph.
02

Plot the line \(y=x\)

On the same graph, plot the line \(y=x\). This is the line that the graphs of the functions will be mirrored across if they are indeed inverses of each other.
03

Check for Reflection

Examine the graphs of the two functions with respect to the line \(y=x\). If the graphs are mirror reflections of one another across this line, the functions are inverses. For any point (a,b) on one graph, there should be a corresponding point (b,a) on the other. If this condition is met, then the functions are indeed inverses of each other.

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