   Chapter 11.1, Problem 25ES ### 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
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# Let f be a real-valued function of a real variable. Show that if f is increasing on a set S and if M is any negative real number, then Mf is decreasing on S.

To determine

To show:

Show that if f is increasing on a set S and if M is any negative real number, then Mf is decreasing on S.

Explanation

Given information:

Let f be a real valued function of a real variable.

Concept used:

Suppose x1 and x2 are particular but arbitrary chosen elements of S such that x1<x2 ,

Calculation:

Suppose x1 and x2 are particular but arbitrary chosen elements of S such that x1<x2 ,

Since f is decreasing function, it follows that

x1<x2f(x1)>f(x2)

Multiplying both sides m>0 ,

Mf(x1)>Mf(x2)

Since multiplying both sides of the inequality by a positive number does not change the direction of the inequality

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