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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

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 decreasing on a set S and if M is any positive real number, then Mf is decreasing on S.

To determine

To show:

Show that if f is decreasing on a set S and if M is any positive 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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Chapter 11 Solutions

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Sect-11.1 P-5ESSect-11.1 P-6ESSect-11.1 P-7ESSect-11.1 P-8ESSect-11.1 P-9ESSect-11.1 P-10ESSect-11.1 P-11ESSect-11.1 P-12ESSect-11.1 P-13ESSect-11.1 P-14ESSect-11.1 P-15ESSect-11.1 P-16ESSect-11.1 P-17ESSect-11.1 P-18ESSect-11.1 P-19ESSect-11.1 P-20ESSect-11.1 P-21ESSect-11.1 P-22ESSect-11.1 P-23ESSect-11.1 P-24ESSect-11.1 P-25ESSect-11.1 P-26ESSect-11.1 P-27ESSect-11.1 P-28ESSect-11.2 P-1TYSect-11.2 P-2TYSect-11.2 P-3TYSect-11.2 P-4TYSect-11.2 P-5TYSect-11.2 P-6TYSect-11.2 P-1ESSect-11.2 P-2ESSect-11.2 P-3ESSect-11.2 P-4ESSect-11.2 P-5ESSect-11.2 P-6ESSect-11.2 P-7ESSect-11.2 P-8ESSect-11.2 P-9ESSect-11.2 P-10ESSect-11.2 P-11ESSect-11.2 P-12ESSect-11.2 P-13ESSect-11.2 P-14ESSect-11.2 P-15ESSect-11.2 P-16ESSect-11.2 P-17ESSect-11.2 P-18ESSect-11.2 P-19ESSect-11.2 P-20ESSect-11.2 P-21ESSect-11.2 P-22ESSect-11.2 P-23ESSect-11.2 P-24ESSect-11.2 P-25ESSect-11.2 P-26ESSect-11.2 P-27ESSect-11.2 P-28ESSect-11.2 P-29ESSect-11.2 P-30ESSect-11.2 P-31ESSect-11.2 P-32ESSect-11.2 P-33ESSect-11.2 P-34ESSect-11.2 P-35ESSect-11.2 P-36ESSect-11.2 P-37ESSect-11.2 P-38ESSect-11.2 P-39ESSect-11.2 P-40ESSect-11.2 P-41ESSect-11.2 P-42ESSect-11.2 P-43ESSect-11.2 P-44ESSect-11.2 P-45ESSect-11.2 P-46ESSect-11.2 P-47ESSect-11.2 P-48ESSect-11.2 P-49ESSect-11.2 P-50ESSect-11.2 P-51ESSect-11.3 P-1TYSect-11.3 P-2TYSect-11.3 P-3TYSect-11.3 P-1ESSect-11.3 P-2ESSect-11.3 P-3ESSect-11.3 P-4ESSect-11.3 P-5ESSect-11.3 P-6ESSect-11.3 P-7ESSect-11.3 P-8ESSect-11.3 P-9ESSect-11.3 P-10ESSect-11.3 P-11ESSect-11.3 P-12ESSect-11.3 P-13ESSect-11.3 P-14ESSect-11.3 P-15ESSect-11.3 P-16ESSect-11.3 P-17ESSect-11.3 P-18ESSect-11.3 P-19ESSect-11.3 P-20ESSect-11.3 P-21ESSect-11.3 P-22ESSect-11.3 P-23ESSect-11.3 P-24ESSect-11.3 P-25ESSect-11.3 P-26ESSect-11.3 P-27ESSect-11.3 P-28ESSect-11.3 P-29ESSect-11.3 P-30ESSect-11.3 P-31ESSect-11.3 P-32ESSect-11.3 P-33ESSect-11.3 P-34ESSect-11.3 P-35ESSect-11.3 P-36ESSect-11.3 P-37ESSect-11.3 P-38ESSect-11.3 P-39ESSect-11.3 P-40ESSect-11.3 P-41ESSect-11.3 P-42ESSect-11.3 P-43ESSect-11.4 P-1TYSect-11.4 P-2TYSect-11.4 P-3TYSect-11.4 P-4TYSect-11.4 P-5TYSect-11.4 P-1ESSect-11.4 P-2ESSect-11.4 P-3ESSect-11.4 P-4ESSect-11.4 P-5ESSect-11.4 P-6ESSect-11.4 P-7ESSect-11.4 P-8ESSect-11.4 P-9ESSect-11.4 P-10ESSect-11.4 P-11ESSect-11.4 P-12ESSect-11.4 P-13ESSect-11.4 P-14ESSect-11.4 P-15ESSect-11.4 P-16ESSect-11.4 P-17ESSect-11.4 P-18ESSect-11.4 P-19ESSect-11.4 P-20ESSect-11.4 P-21ESSect-11.4 P-22ESSect-11.4 P-23ESSect-11.4 P-24ESSect-11.4 P-25ESSect-11.4 P-26ESSect-11.4 P-27ESSect-11.4 P-28ESSect-11.4 P-29ESSect-11.4 P-30ESSect-11.4 P-31ESSect-11.4 P-32ESSect-11.4 P-33ESSect-11.4 P-34ESSect-11.4 P-35ESSect-11.4 P-36ESSect-11.4 P-37ESSect-11.4 P-38ESSect-11.4 P-39ESSect-11.4 P-40ESSect-11.4 P-41ESSect-11.4 P-42ESSect-11.4 P-43ESSect-11.4 P-44ESSect-11.4 P-45ESSect-11.4 P-46ESSect-11.4 P-47ESSect-11.4 P-48ESSect-11.4 P-49ESSect-11.4 P-50ESSect-11.4 P-51ESSect-11.5 P-1TYSect-11.5 P-2TYSect-11.5 P-3TYSect-11.5 P-4TYSect-11.5 P-5TYSect-11.5 P-1ESSect-11.5 P-2ESSect-11.5 P-3ESSect-11.5 P-4ESSect-11.5 P-5ESSect-11.5 P-6ESSect-11.5 P-7ESSect-11.5 P-8ESSect-11.5 P-9ESSect-11.5 P-10ESSect-11.5 P-11ESSect-11.5 P-12ESSect-11.5 P-13ESSect-11.5 P-14ESSect-11.5 P-15ESSect-11.5 P-16ESSect-11.5 P-17ESSect-11.5 P-18ESSect-11.5 P-19ESSect-11.5 P-20ESSect-11.5 P-21ESSect-11.5 P-22ESSect-11.5 P-23ESSect-11.5 P-24ESSect-11.5 P-25ESSect-11.5 P-26ES