/*! 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 5 Find the domain of each rational... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 5

Find the domain of each rational function. $$h(x)=\frac{x+7}{x^{2}-49}$$

Short Answer

Expert verified
The domain of the function is all real numbers except 7 and -7. So, \(x \in R, x \neq 7, -7\).

Step by step solution

01

Set the denominator equal to zero

The first step is to set the denominator equal to zero, so \(x^{2}-49 = 0\). This is because we want to find the values of x which make the denominator zero so we can exclude them from the domain.
02

Solve for x

You can solve this equation by taking the square root of both sides to get \(x = \sqrt{49} = 7\) and \(x = -\sqrt{49} = -7\). So, x = 7 and x = -7 are the values that make the denominator zero.
03

Exclude the values from the domain

The domain of the function is all real numbers except the ones that make the denominator zero. So the values 7 and -7 need be excluded from the domain. This can be written as \(x \in R, x \neq 7, -7\)

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

A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Six hundred feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum area?

Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{2}-4}{x}$$

Describe how to find a parabola's vertex if its equation is in the form \(f(x)=a x^{2}+b x+c .\) Use \(f(x)= x^{2}-6 x+8\) as an example.

The perimeter of a rectangle is 180 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 800 square feet.

Write a polynomial inequality whose solution set is \([-3,5]\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Pure 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.