BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.7, Problem 92E
To determine

To show: fI=f, If=f and ff1=f1f=I

Expert Solution

Explanation of Solution

Given information: I(x)=x

Formula used: f(x)g(x)=f(g(x))

Proof:

  I(x)=x

  fI=f(x)I(x)=f(I(x))=f(x)=ffI=f

  If=I(x)f(x)=I(f(x))        [I(x)=x]=f(x)=fIf=f

   ff1=f(f1(x))=x=I

   f1f=f1(f(x))=x=I

From above two we can reach at the conclusion that ff1f1f=I

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