# The formula for f n ( 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, Problem 19P
To determine

## To find: The formula for fn(x).

Expert Solution

The formula for fn(x) is fn(x)=x2n+1.

### Explanation of Solution

Given:

f0(x)=x2

fn+1(x)=f0(fn(x)) where n = 0,1,2……

Calculation:

Consider fn+1(x)=f0(fn(x)) (1)

Substitute 0 for n in equation (1),

f0+1(x)=f0(f0(x))f1(x)=f0(f0(x))=f0(x2)=x4

Substitute 1 for n in equation (1),

f1+1(x)=f0(f1(x))f2(x)=f0(f1(x))=f0(x4)=x8

Substitute 2 for n in equation (1),

f2+1(x)=f0(f2(x))f3(x)=f0(f2(x))=f0(x8)=x16

Proceeding this way continuous,

fn(x)=x2n+1

Thus, the formula for fn(x) is fn(x)=x2n+1, where n=1,2,3,.

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