# The value of f − 1 ( 3 ) and f ( f − 1 ( 2 ) ) if f ( x ) = x 5 + x 3 + x .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.6, Problem 16E
To determine

## To find: The value of f−1(3) and f(f−1(2)) if f(x)=x5+x3+x .

Expert Solution

The value of f1(3)=1 .

The value of  f(f1(2))=2 .

### Explanation of Solution

The given function is f(x)=x5+x3+x .

Notice that the value of f(1)=3 as, 15+13+1=3 .

According to the definition of an inverse function, f1(y)=x if and only if f(x)=y where f is one-to-one.

The value of f1(3)=1 since f(1)=3 .

Express  f(f1(2)) as  f1(f(2)) .

Apply the cancellation equation of the inverse function and obtain  f1(f(2))=2 .

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