/*! 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 17 Find the domain of each function... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 17

Find the domain of each function. $$f(x)=\sqrt{x-3}$$

Short Answer

Expert verified
The domain of the function \(f(x) = \sqrt{x - 3}\) is \(x \geq 3\).

Step by step solution

01

Identify the Constraint from the Function

Start off by noting that the function contains a square root. A square root function domain is only defined for values \(\geq 0\), because we can't take the square root of a negative number in the real number system.
02

Set up Inequality

To find the domain of the function, set the value under the square root, \(x-3\), to be greater than or equal to 0. This results in the inequality \(x - 3 \geq 0\) which we need to solve.
03

Solve the Inequality

Solving the inequality \(x - 3 \geq 0\) gives \(x \geq 3\). This represents the set of all \(x\) values for which the function is defined.

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

graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$ \begin{aligned} x^{2}+y^{2} &=9 \\ x-y &=3 \end{aligned} $$

give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$ x^{2}+(y-2)^{2}=4 $$

(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.

use a graphing utility to graph each function. Use \(a[-5,5,1]\) by \([-5,5,1]\) viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$ g(x)=\left|4-x^{2}\right| $$

What is a relation? Describe what is meant by its domain and its range.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Statistics

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.