# 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 36E
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)=x53x+4 and g(x)=5+4x13x

Calculation:

Now:

g(f(x))=g(x53x+4)g(f(x))=5+4(x53x+4)13(x53x+4)g(f(x))=15x+20+4x203x+43x+43x+153x+4g(f(x))=20x20=x

f(g(x))=f(5+4x13x)f(g(x))=5+4x13x53(5+4x13x)+4f(g(x))=5+4x5+15x13x15+12x+412x13xf(g(x))=20x20=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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