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Chapter 2: Problem 74

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 be used to determine visually if two functions are inverses of each other by graphing them along with the line \( y = x \). If the graphs of the two functions are symmetrical about the line \( y = x \), then they are inverses of each other.

Step by step solution

01

Plot Function Graphs

Use a graphing utility to plot the graphs of the two functions being considered. Make sure to cover the same interval on the x-axis for both functions.
02

Plot Identity Line

Plot the line \( y = x \) on the same graph. This line is the line of symmetry for inverse functions.
03

Identify Symmetry

Visually examine the graph. If the graphs of the two functions are reflections of each other across the line \( y = x \), then they are inverses of each other.

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Most popular questions from this chapter

Begin by graphing the standard cubic function, \(f(x)-x^{3} .\) Then use transformations of this graph to graph the given function. $$ g(x)-(x-2)^{3} $$

In Tom Stoppard's play Arcadia , the characters dream and talk about mathematics, including ideas involving graphing. composite functions, symmetry, and lack of symmetry in things that are tangled, mysterious, and unpredictable. Group members should read the play. Present a report on the ideas discussed by the characters that are related to concepts that we studied in this chapter. Bring in a copy of the play and read appropriate excerpts.

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Use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$ f(x)=\sqrt[3]{2-x} $$

Use a graphing utility to graph each function. Use a \([-5,5,1]\) by \([-5,5,1]\) viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$h(x)=|x-2|+|x+2|$$
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