/*! 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} Problem 77 Use a graphing utility to graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 77

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). $$f(x)=\sqrt[3]{2-x}$$

Short Answer

Expert verified
Yes, the function \(f(x)=\sqrt[3]{2-x}\) has an inverse that is also a function, meaning the function is one-to-one.

Step by step solution

01

Plotting the function

Start by plotting the function \(f(x)=\sqrt[3]{2-x}\) using a graphing utility. This type of function will typically resemble a curve due to the cubic root. Since \(f(x)\) is defined everywhere, the domain is all real numbers.
02

Checking for one-to-oneness using Horizontal Line Test

Apply the Horizontal Line Test to the graph. If no horizontal line intersects the graph more than once, then the function is one-to-one. Otherwise, if any horizontal line intersects the graph more than once, the function is not a one-to-one function.
03

Conclusion

After doing the Horizontal Line Test, you will find that no horizontal line intersects the graph of the function more than once. Hence, \(f(x) = \sqrt[3]{2-x}\) is a one-to-one function and has an inverse that is also a function.

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

(For assistance with this exercise, refer to the discussion of piecewise functions beginning on page 234 , as well as to Exercises \(79-80 .\) ) Group members who have cellphone plans should describe the total monthly cost of the plan as follows: \(\$ ________\) per month buys ____________ minutes. Additional time costs $\$$ __________per minute.

determine whether each statement makes sense or does not make sense, and explain your reasoning. To avoid sign errors when finding \(h\) and \(k,\) I place parentheses around the numbers that follow the subtraction signs in a circle's equation.

In Exercises \(105-108,\) you will be developing functions that model given conditions. A car was purchased for \(\$ 22,500\). The value of the car decreased by \(\$ 3200\) per year for the first six years. Write a function that describes the value of the car, \(V,\) after \(x\) years, where \(0 \leq x \leq 6 .\) Then find and interpret \(V(3)\)

Exercises \(98-100\) will help you prepare for the material covered in the first section of the next chapter. In Exercises \(98-99,\) solve each quadratic equation by the method of your choice. Use the graph of \(f(x)=x^{2}\) to graph \(g(x)=(x+3)^{2}+1\)

Exercises \(98-100\) will help you prepare for the material covered in the first section of the next chapter. In Exercises \(98-99,\) solve each quadratic equation by the method of your choice. $$ -x^{2}-2 x+1=0 $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

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.