/*! 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 29 Evaluate (if possible) the funct... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 29

Evaluate (if possible) the function at each specified value of the independent variable and simplify. \(f(x)=|x| / x\) (a) \(f(2)\) (b) \(f(-2)\) (c) \(f(x-1)\)

Short Answer

Expert verified
(a) \(f(2) = 1\); (b) \(f(-2) = -1\); (c) \(f(x-1) = |x-1| / (x-1)\), undefined when \(x=1\)

Step by step solution

01

Evaluate for \(f(2)\)

Insert \(x=2\) into \(f(x)=|x| / x\). Since 2 is positive, the absolute value doesn't change the value so we get \(f(2)= (2) / 2 = 1\)
02

Evaluate for \(f(-2)\)

Insert \(x=-2\) into \(f(x)=|x| / x\). Since -2 is negative, the absolute value changes the sign, so we get \(f(-2)= |-2| / (-2) = 2 / -2 = -1\)
03

Evaluate for \(f(x-1)\)

Insert \(x=x-1\) into \(f(x)=|x| / x\). As we don't know the exact value of \(x-1\), the function results in \(f(x-1)= |x-1| / (x-1)\). Note that this function will be undefined when \(x=1\) as it results in division by zero.

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

The work \(W\) done when lifting an object varies jointly with the object's mass \(m\) and the height \(h\) that the object is lifted. The work done when a 120 -kilogram object is lifted 1.8 meters is 2116.8 joules. How much work is done when lifting a 100 -kilogram object 1.5 meters?

Sketch the graph of the function. $$f(x)=\left\\{\begin{array}{ll}x^{2}+5, & x \leq 1 \\\\-x^{2}+4 x+3, & x>1\end{array}\right.$$

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.

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?

(a) use a graphing utility to graph the function and (b) state the domain and range of the function. $$s(x)=2\left(\frac{1}{4} x-\left[\frac{1}{4} x\right]\right)$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Decision 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.