Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 5

If \(0

Short Answer

Expert verified
The correct statement is \(\sqrt{x}<x<1\).

Step by step solution

01

Examine option 1

This option suggests that \(x<\sqrt{x}<1\). Remembering that the square root function is increasing in the interval \((0, 1)\), this means that a number will always be less than its square root. However, this is not true in the interval \((0, 1)\), where a number is greater than its square root. Hence, this option is incorrect.
02

Examine option 2

Option 2 suggests \(x<1<\sqrt{x}\). This suggests that for \(0<x<1\), the square root of \(x\) is greater than 1. This is not true because when \(0<x<1\), \(x\) is less than 1 and hence, its square root is also less than 1. Hence, this option is not correct.
03

Examine option 3

Looking at option 3, \(\sqrt{x}<x<1\), it can be seen that this is indeed true. In the range \(0<x<1\), \(x\) is indeed greater than its square root and less than 1. Hence, this is the correct response option.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

If \(x=\sqrt{25}\), which of the following is true? $$ \begin{aligned} & \text { C } x=5 \\ & x=-5 \\ & x=\pm 5 \\ & \text { I don't know. } \\ & \end{aligned} $$

Line 1 is defined by \(y=3 x+7\), and line 2 is parallel to line 1 . What is the slope of line 2 ? O \(-3\) 03 O \(\frac{1}{3}\) I don't know.

If \(x^2=25\), which of the following is true? $$ \begin{aligned} & \bigcirc x=5 \\ & \bigotimes x=-5 \\ & \hdashline x=\pm 5 \\ & \text { idon't know. } \end{aligned} $$

Even integer q is the product of two distinct prime numbers. What can you say about the factors of q?

If \(x<0\), which of the following is true? \(O x^2\) is positive. \(x^2\) is negative. \(x^2\) could be either positive or negative. I don't know.
See all solutions

Recommended explanations on English Textbooks

History of English Language

Read Explanation

Blog

Read Explanation

Prosody

Read Explanation

Summary Text

Read Explanation

Research and Composition

Read Explanation

Pragmatics

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.

Sign-up for free