   Chapter 7.3, Problem 10ES ### 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

# Define F : Z → Z and G : Z → Z by the rules F ( n ) = 2 n and G ( n ) = ⌊ n / 2 ⌋ for every integer n. a. Find ( G ∘ F ) ( 8 ) , ( F ∘ G ) ( 8 ) , ( G ∘ F ) ( 3 ) , and ( F ∘ G ) ( 3 ) . b. Is G ∘ F = F ∘ G ? Explain.

To determine

(a)

To find:

The values of (GF)(8), (FG)(8), (GF)(3) and (FG)(3).

Explanation

Given information:

F(n)=2nG(n)=n2

Concept used:

fg(x)=f{g(x)}

Calculation:

(GF)(8)=G{F(8)}=G(8×2)=G(16)=162=8=8

(FG)(8)=F{G(8)}=F{82}=F(4)=2×4=8

(GF)(3</

To determine

(b)

To check:

Whether GF equals FG and also give explanation.

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