/*! 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 zeros of the function a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 17

Find the zeros of the function algebraically. $$f(x)=\frac{x}{9 x^{2}-4}$$

Short Answer

Expert verified
The zero of the function \(f(x)=\frac{x}{9 x^{2}-4}\) is at point \(x=0\).

Step by step solution

01

Set Up The Equation

To find the zeros of the function \( f(x) \), one should set up the equation \( f(x)=0 \). Substituting \( f(x) \) with its given form, the equation becomes \(\frac{x}{9 x^{2}-4} = 0\).
02

Solve The Equation

The main part is solving the equation, and these are the steps:- First, clear the denominator of the fraction by multiplying both sides of the equation by \(9x^{2}-4\). This will yield the equation \(x=0\).- Then, solve for \(x\). In this case, the zero of the function is \(x=0\).
03

Check The Denominator

Ensure that the denominator of the function is not zero for the value of \(x\) found above. So, place \(0\) into the denominator \(9x^{2}-4\). Upon simplifying, you will find that the denominator is not zero. Therefore, \(x=0\) is a valid zero of the 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

Write the area \(A\) of a square as a function of its perimeter \(P\).

Finding a Mathematical Model In Exercises \(41-50\), find a mathematical model for the verbal statement. For a constant temperature, the pressure \(P\) of a gas is inversely proportional to the volume \(V\) of the gas.

A company produces a product for which the variable cost is 12.30 dollars per unit and the fixed costs are 98,000 dollars. The product sells for 17.98 dollars. Let \(x\) be the number of units produced and sold. (a) The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost \(C\) as a function of the number of units produced. (b) Write the revenue \(R\) as a function of the number of units sold. (c) Write the profit \(P\) as a function of the number of units sold. (Note: \(P=R-C\) ).

Sketch the graph of the function. $$h(x)=\left\\{\begin{array}{ll}4-x^{2}, & x<-2 \\\3+x, & -2 \leq x<0 \\\x^{2}+1, & x \geq 0\end{array}\right.$$

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$h(x)=\sqrt{x+2}+3$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Applied 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.