/*! 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 2 In your own words, define the do... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 2

In your own words, define the domain of a function and give an example.

Short Answer

Expert verified
The domain of a function is the set of all input values (x-values) that do not cause mathematical errors. For instance, the domain of \( f(x) = \frac{1}{x} \) is all real numbers except 0.

Step by step solution

01

- Understand the Concept of Domain

The domain of a function refers to all the possible input values (usually represented by 'x') that the function can accept without causing any mathematical errors. Think of it as the complete set of valid x-values.
02

- Identify Common Domain Restrictions

Certain mathematical operations have restrictions. For example, you can't divide by zero and you can't take the square root of a negative number in real numbers. These restrictions help define the domain.
03

- Write Down a General Definition

In your own words, the domain of a function is the set of all x-values that you can input into the function without causing mathematical errors or undefined operations.
04

- Provide an Example

Consider the function \( f(x) = \frac{1}{x} \). To find the domain, identify the values of x that make the denominator zero. In this case, x cannot be zero because division by zero is undefined. Therefore, the domain of \( f(x) = \frac{1}{x} \) is all real numbers except 0.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

headline of the respective core concept
A function's domain represents all the input values (commonly denoted as 'x') that the function can accept without running into mathematical problems or errors. It's essential to grasp this because only certain values will keep the function valid and operational.

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

Find the midpoint of each segment with the given endpoints. $$ (2.5,3.1) \text { and }(1.7,-1.3) $$

An equation that defines \(y\) as a function fof \(x\) is given. (a) Solve for \(y\) in terms of \(x,\) and \(r e-\) place \(y\) with the function notation \(f(x) .\) (b) Find \(f(3) .\) See Example 6. $$ x-4 y=8 $$

For each situation, (a) write an equation in the form \(y=m x+b,(b)\) find and interpret the ordered pair associated with the equation for \(x=5,\) and \((c)\) answer the question. For a family membership, the athletic club in Exercise 83 charges a membership fee of S159, plus \(\$ 60\) for each additional family member after the first. Let \(x\) represent the number of additional family members and \(y\) represent the cost. What is the membership fee for a four-person family?

Write an equation in the form \(y=m x\) for each situation. Then give the three ordered pairs associated with the equation for x-values 0,5, and 10. See Example 7(a). \(x\) represents the number of gallons of gas sold at \(\$ 3.10\) per gal, and \(y\) represents the total cost of the gasoline (in dollars).

An equation that defines \(y\) as a function fof \(x\) is given. (a) Solve for \(y\) in terms of \(x,\) and \(r e-\) place \(y\) with the function notation \(f(x) .\) (b) Find \(f(3) .\) See Example 6. $$ y-3 x^{2}=2 $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Geometry

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.