   Chapter 7.3, Problem 12ES ### 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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# The functions of each pair in 12—14 are inverse to each other. For each pair, check that both compositions give the identity function. 12. F : R → R and F − 1 : R → R are defined by F ( x ) = 3 x + 2 and F − 1 ( y ) = y − 2 3 , for every y ∈ R .

To determine

To check:

Whether both the compositions FF1 and F1F are identity functions.

Explanation

Given information:

F: and F1: are defined by,

F(x)=3x+2 and F1(y)=y23, for all y.

Concept used:

f(x)=yx=f1(y)

Calculation:

The two functions F and F1 are defined by,

F(x)=3x+2x and F1(y)=y23y

The objective is to check the both compositions give the identity function.

For any x, compute the composition: (FF1)(x) as follows.

(FF 1)(x)=F(F 1(x))        By the definition of compositions=F( x23)          Since F1(y)=y23 and replace y by x=3( x23)+2      Since F(x)=3x+2 and replace x by x23=x

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