Question

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

Name: Problem 28, Chapter 7: Calculus: One Variable
Uploaded: 2021-12-18T02:55:11-08:00
Duration: 2 min
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 28

Instant Answer

Solved by Expert Gregory Higby

12/18/2021

Step 1

The y-intercept is at (0,1) and the x-intercept is at some point to the left of -1, which we will denote as (-a,0). Show more…

Show all steps

Thanks for your feedback!

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

Play audio

Feedback

Gregory Higby and 91 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Inverse Function

An inverse function reverses the operation of the original function. If a function f maps an input x to an output y, then its inverse function, denoted as f?¹, maps y back to x. The inverse exists only if f is one-to-one, meaning each output is produced by exactly one input.

Reflection across the Line y = x

A key graphical property of inverse functions is that their graphs are mirror images of each other with respect to the line y = x. Reflecting the graph of a function across this line swaps the roles of x and y, which is equivalent to finding the inverse function.

Domain and Range Swap

In the context of inverse functions, the domain (set of possible input values) of the original function becomes the range (set of possible output values) of its inverse, and vice versa. This is important when sketching the graph since the spread of the graph is rearranged along the axes.

Please give Ace some feedback