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

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 2

Find the domain of each rational function. $$ f(x)=\frac{7 x}{x-8} $$

Short Answer

Expert verified
The domain of the function \(f(x) = \frac{7x}{x-8}\) is all real numbers except 8 or \((-\infty, 8) \cup (8, \infty)\) in interval notation.

Step by step solution

01

Identify the denominator

In the function, \(f(x) = \frac{7x}{x-8} \), the denominator is \(x-8 \). The denominator is the part of the function we need pay special attention to in order to identify the domain of the function.
02

Set the denominator equal to zero and solve for x

To find what x-values should be excluded from the domain, we need to solve the equation where the denominator equals zero. So, we solve \(x-8 = 0\), this gives \(x = 8\).
03

Identify the domain

By knowing the x-value that makes the denominator zero, we can identify the domain of the function. The domain will include all real numbers except 8. In interval notation, this can be expressed as \((-\infty, 8) \cup (8, \infty)\).

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

Crosses the \(x\)-axis at \(-4,0,\) and \(3 ;\) lies above the \(x\)-axis between \(-4\) and \(0 ;\) lies below the \(x\)-axis between 0 and 3

Use long division to rewrite the equation for \(g\) in the form $$ \text {quotient}+\frac{\text {remainder}}{\text {divisor}} $$ Then use this form of the function's equation and transformations \( \text { of } f(x)=\frac{1}{x} \text { to graph } g \). $$ g(x)=\frac{3 x-7}{x-2} $$

In Exercises 94鈥�97, use a graphing utility with a viewing rectangle large enough to show end behavior to graph each polynomial function. $$f(x)=-x^{4}+8 x^{3}+4 x^{2}+2$$

Use a graphing utility with a viewing rectangle large enough to show end behavior to graph each polynomial function. \(f(x)=-x^{5}+5 x^{4}-6 x^{3}+2 x+20\)

Write an equation in point-slope form and slope-intercept form of the line passing through \((-10,3)\) and \((-2,-5)\) (Section \(2.3,\) Example 3 )
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

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.