Question

Sketch the graph of the inverse of the function graphed below. (FIGURE CANNOT COPY)

Name: Problem 30, Chapter 7: Calculus: One Variable
Uploaded: 2021-12-18T13:39:24-08:00
Duration: 1 min 58 s
Channel: Gregory Higby
Description: Sketch the graph of the inverse of the function graphed below. (FIGURE CANNOT COPY)

   Sketch the graph of the inverse of the function graphed below.
(FIGURE CANNOT COPY)

Calculus: One Variable

Garret J. Etgen,… 10th Edition

Chapter 7, Problem 30

Instant Answer

Solved by Expert Gregory Higby

12/18/2021

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From the explanation, we can see that the points are (0,0) and (1,1). Show more…

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Sketch the graph of the inverse of the function graphed below. (FIGURE CANNOT COPY)

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Key Concepts

Inverse Function

An inverse function reverses the effect of the original function. It is defined so that applying the function and its inverse in succession returns the original input. In other words, if f(x) maps x to y, the inverse function f?¹(y) maps y back to x.

Graphing the Inverse

Graphing an inverse function typically involves reflecting the graph of the original function across the line y = x. This method works because in the inverse, the roles of the x and y coordinates are exchanged, so a point (a, b) on the original graph becomes (b, a) on the inverse graph.

Reflection Across the Line y = x

The line y = x plays a central role in finding the inverse graphically. Reflecting a function's graph over this line swaps each point's coordinates, which is exactly what the inverse function does algebraically. This reflection technique provides a visual means to derive and sketch the inverse function from the original graph.

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