   Chapter 7.3, Problem 17ES ### 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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# Prove Theorem 7.3.2(b): If f : X → Y is a one-to-one and onto function with inverse function f − 1 : Y → X , then f ∘ f − 1 = 1 y , where I y is the identity function on Y.

To determine

To Prove:

If a functionf:XY  is one-to-one and onto function having its inverse function f1:YX, then ff1=IY, where IY is the identity function on Y.

Explanation

Given information:

f:XY is a one and onto function with inverse function f1:YX.

Concept used:

fog(x)=f(g(x)).

Proof:

Suppose f:XY  is a one to one and onto function with inverse function f1:YX.

To show that ff1=IY, we must show that for all yY, (ff1)(y)=y.

Let y be any element in Y and let f1(y)=x.

If xX then y=f(x)

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