   Chapter 11.1, Problem 20ES ### 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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# Given real-valued functions f and g with the same domain D, the sum of f and g, denoted f + g , is defined as follows: For each real number x ,   ( f + g ) ( x ) = f ( x ) + g ( x ) .Show that if f and g are both increasing on a set S. then f + g is also increasing on S.

To determine

To show:

If f and g are both increasing on a set S, then f+g is also increasing on S.

Explanation

Given information:

Suppose f:RR is increasing.

Concept used:

Given real valued functions f and g with the same domain D, the sum of f and g, denoted f+g, is defined as follows.

For all real numbers x,(f+g)(x)=f(x)+g(x).

Calculation:

It is given that f and g are real valued functions defined on the same domain D. Let SCD where S a non-empty subset of is D.

f Is an increasing function on a set, so for x1x2S if x1<x2f(x1)<f(x2).....(1).

g Is an increasing function on a set, so for x1x2S if x1<x2g(x1)<g(x2).....(2)

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