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 35E
To determine

To prove f and g are inverse of each other

Expert Solution

Answer to Problem 35E

By the property of inverse functions f and g are inverse of each other

Explanation of Solution

Given information:

  f(x)=x+2x2 and g(x)=2x+2x1

Calculation:

Now:

  g(f(x))=g(x+2x2)g(f(x))=2(x+2x2)+2x+2x21g(f(x))=2x+4x2+2(x2)x2x+2x21(x2)x2g(f(x))=2x+4+2x4x2x+2x+2x2

  g(f(x))=4x4g(f(x))=x

  f(g(x))=f(2x+2x1)f(g(x))=2x+2x1+22x+2x12f(g(x))=2x+2x1+2x2x12x+2x12x+2x1f(g(x))=4x4=x

So by property of inverse functions f and g are inverses of each other.

These equations when composed cancel each other

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