   Chapter 7.3, Problem 11ES ### 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 : R → R and G : R → R by the rules F ( n ) = 3 x and G ( n ) = ⌈ x / 3 ⌉ for every number x. a. Find ( G ∘ F ) ( 6 ) , ( F ∘ G ) ( 6 ) , ( G ∘ F ) ( 1 ) , and ( F ∘ G ) ( 1 ) . b. Is G ∘ F = F ∘ G ? Explain.

To determine

(a)

To find:

The values of (GF)(6), (FG)(6), (GF)(1) and (FG)(1).

Explanation

Given information:

F(x)=3xG(x)=x3

Concept used:

FG(x)=F{G(x)}

Calculation:

(GF)(6)=G{F(6)}=G(3×6)=G(18)=183=6=6

(FG)(6)=F{G(6)}=F( 6 3)=F(2)=F(2)=2×3=6

To determine

(b)

To check:

Whether GF equals FG and also give explanation.

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