Problem

Use the given graph of $ f $ to sketch the graph …

00:52

Problem 29 Medium Difficulty

Use the given graph of $ f $ to sketch the graph of $ f^{-1} $.

Answer

Reflect the graph of $f$ about the line $y=x$. The points (-1,-2),(1,-1) $(2,2),$ and (3,3) on $f$ are reflected to $(-2,-1),(-1,1),(2,2),$ and (3,3) on $f^{-1}$

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00:53

Jeffrey P.

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

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Johns Hopkins University

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Video Transcript

here were given a rough sketch of the graph of F, and we want to graph f inverse. So let's look at some of the key points on F. It goes through the point. Negative one negative, too. One negative one to to 33 So if in verse, will have those coordinates switched. So if inverse will go through negative to negative one negative 11 to to and 33 So let's start by plotting those points negative to negative one. Negative. 11 2233 Let's connect those with line segments. And now what we should observe is that these graphs are reflections across the line. Y equals X. Here's the line Y equals X. They do, indeed to look like appear to look like reflections across that line.

Heather Z.

Oregon State University

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Top Calculus 3 Educators

Lily A.

Johns Hopkins University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

Michael J.

Idaho State University