/*! 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 58 Use a graphing utility to graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 58

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). $$f(x)=(x-1)^{3}$$

Short Answer

Expert verified
The function \(f(x) = (x-1)^3\) is one-to-one, and therefore, it has an inverse that is also a function.

Step by step solution

01

Graph the function

Start by plotting the function \(f(x) = (x-1)^3\). This is a basic cubic function shifted one unit to the right. Plot the function using a graphing utility. This will give a visual representation of the function.
02

Analyze the graph

Observe the graph to see if any horizontal line intersects the function at more than one point. If it does, the function is not one-to-one. If each horizontal line intersects the function at most once, the function is one-to-one. This is called the Horizontal Line Test.
03

Conclusion

If no horizontal line intersects the graphed function at more than one point, we can say that the function \(f(x) = (x-1)^3\) is indeed one-to-one, and thus, it 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

The number of lawyers in the United States can be modeled by the function $$ f(x)=\left\\{\begin{array}{ll} 6.5 x+200 & \text { if } 0 \leq x<23 \\ 26.2 x-252 & \text { if } x \geq 23 \end{array}\right. $$ where \(x\) represents the number of years after 1951 and \(f(x)\) represents the number of lawyers, in thousands. In Exercises \(85-88,\) use this function to find and interpret each of the following. $$ f(10) $$

During a particular year, the taxes owed, \(T(x),\) in dollars, filing separately with an adjusted gross income of \(x\) dollars is given by the piecewise function $$ T(x)=\left\\{\begin{array}{ll} 0.15 x & \text { if } 0 \leq x<17,900 \\ 0.28(x-17,900)+2685 & \text { if } 17,900 \leq x<43,250 \\ 0.31(x-43,250)+9783 & \text { if } x \geq 43,250 \end{array}\right. $$ In Exercises \(89-90,\) use this function to find and interpret each of the following. $$ T(40,000) $$

Then use the TRACE feature to trace along the line and find the coordinates of two points. Use these points to compute the line's slope. Check your result by using the coefficient of \(x\) in the line's equation. $$y=-3 x+6$$

Assume that \((a, b)\) is a point on the graph of \(f .\) What is the corresponding point on the graph of each of the following functions? $$ y=f(x)-3 $$

Prove that the equation of a line passing through \((a, 0)\) and \((0, b)(a \neq 0, b \neq 0)\) can be written in the form \(\frac{x}{a}+\frac{y}{b}=1 .\) Why is this called the intercept form of a line?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

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.