/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 57 In the following exercise, find ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q. 57 (page 1005)

In the following exercise, find the inverse of each function.

fx=x-33

Short Answer

Expert verified

The inverse of the given function isf-1x=x3+3

Step by step solution

01

Step 1. Given information   

The given function isfx=x-33

02

Step 2. Interchange the variable  x and y

Substituting fx=y, we get:

y=x-33

Interchanging the variable xand y, we get:

x=y-33

03

Step 3. Solve for y

Solving for y, we get:

x=y-33x3=y-3y=x3+3

substituting y=f-1x, we get:

f-1x=x3+3

04

Step 4. Verify that the functions are inverses. 

Substituting fxin f-'1fx=x, we get:

f-1fx=xf-1x-33=xx-332+3=xx-3+3=xx=x

This is True

Substituting f-1xinff-1x=x, we get:

ff-1x=xfx3+3=xx3+3-33=xx33=xx=x

This is true.

Thus, the obtained inverse is correct

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Convert each logarithmic equation to exponential form:

4=logx81.

In the following exercises, find the inverse of each function.

f(x)=x2+6,x鈮�0

Graph: g(x)=(15)x

In the following exercises, graph each exponential function.

g(x)=3x

Edgar accumulated $5000in credit card debt. If the interest rate is 20%per year, and he does not make any payments for 2years, how much will he owe on this debt in 2years by each method of compounding?

a. compound quarterly

b. compound monthly

c. compound continuously.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.