   Chapter 11.1, Problem 18ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# Let k :   R → R be the function defined by the formula k ( x ) = ( x − 1 ) / x for each real number x ≠ 0 . a. Show that k is increasing for every real number x > 0 . b. Is k increasing or decreasing for x < 0 ? Prove your answer.

To determine

(a)

To show:

k is increasing for all real numbers x>0.

Explanation

Given information:

Let k:RR be the function defined by the formula k(x)=(x1)/x for all real numbers x0.

Concept used:

x1 and x2 Are real numbers with x1<x2<0.

Calculation:

Since x1<x2

x2<x1 By multiplying by 1 and by the order of the inequality

x1x2x2<x1x2x1 By adding x1x2 to both sides

x2(x11)<x1(x21) By factoring both sides

x11x1<x21x2 By dividing both sides by the positive numbers x1x2

To determine

(b)

To show:

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