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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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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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