# Whether the statement, if f and g are functions, then f ∘ g = g ∘ f is true or false. ### 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 6RQ
To determine

## Whether the statement, if f and g are functions, then f∘g=g∘f is true or false.

Expert Solution

Solution:

The statement is false.

### Explanation of Solution

The given statement is false since the below example disproves the given statement.

Let the functions be f(x)=2x2 and g(x)=x1.

The composition function (fg)(x) is defined as (fg)(x)=f(g(x)).

Obtain the value of fg.

f(g(x))=f(x1)=2(x1)2=2(x22x+1)=2x24x+2

Similarly, find the value of gf as follows.

g(f(x))=g(2x2)=2x21

Thus, fggf.

Therefore, the given statement is false.

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