/*! 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 23 Find the zeros of the function a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 23

Find the zeros of the function algebraically. $$f(x)=\sqrt{2 x}-1$$

Short Answer

Expert verified
The zero of the function \(f(x)=\sqrt{2x}-1\) is \(x=0.5\).

Step by step solution

01

Set the Function to zero

In this step, the function \(f(x)=\sqrt{2x}-1\) is set to zero, resulting in the equation: \[\sqrt{2x}-1=0\]. Setting a function to zero is the standard method of finding its roots.
02

Solve for x

In this step, the equation \(\sqrt{2x} - 1= 0\) is rearranged to solve for \(x\). First, add 1 to both sides of the equation: \[\sqrt{2x}=1\]. Then, square both sides to get rid of the square root: \[2x=1\]. Finally, divide both sides of the equation by 2 in order to isolate \(x\): \[x=0.5\]
03

Verify the solution

To verify that \(x=0.5\) is indeed a correct solution, it should be substituted back into the original function and confirm that it results in 0: \[f(0.5)=\sqrt{2(0.5)}-1=0.\] Therefore, \(x=0.5\) is a correct solution.

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

Finding a Mathematical Model In Exercises \(41-50\), find a mathematical model for the verbal statement. Newton's Law of Universal Gravitation: The gravitational attraction \(F\) between two objects of masses \(m_{1}\) and \(m_{2}\) is jointly proportional to the masses and inversely proportional to the square of the distance \(r\) between the objects.

Decide whether the statement is true or false. Justify your answer. A. Given that \(y\) varies directly as the square of \(x\) and \(x\) is doubled, how will \(y\) change? Explain. B. Given that \(y\) varies inversely as the square of \(x\) and \(x\) is doubled, how will \(y\) change? Explain.

Wages A mechanic's pay is 14.00 dollars per hour for regular time and time- and-a-half for overtime. The weekly wage function is \(W(h)=\left\\{\begin{array}{ll}14 h, & 040\end{array}\right.\) where \(h\) is the number of hours worked in a week. (a) Evaluate \(W(30), W(40), W(45),\) and \(W(50)\) (b) The company increased the regular work week to 45 hours. What is the new weekly wage function?

Find the difference quotient and simplify your Answer: $$f(x)=5 x-x^{2}, \quad \frac{f(5+h)-f(5)}{h}, \quad h \neq 0$$

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

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

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.