# To prove f and g are inverse of each other ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

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

#### Solutions

Chapter 2.7, Problem 32E
To determine

## To prove f and g are inverse of each other

Expert Solution

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

### Explanation of Solution

Given information:

f(x)=x3+1 and g(x)=(x1)13

Calculation:

Now:

g(f(x))=g(x3+1) g(f(x))= ( x 3 +11) 1 3 g(f(x))= ( x 3 ) 1 3 g(f(x))=x

f(g(x))=f[ (x1) 1 3 ] f(g(x))= [ (x1) 1 3 ] 3 +1f(g(x))=x1+1f(g(x))=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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