# Whether the statement, if f is a function, then f ( 3 x ) = 3 f ( x ) 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 3RQ
To determine

## Whether the statement, if f is a function, then f(3x)=3f(x) 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 function be f(x)=2x2.

Obtain the value of f(3x) and 3f(x).

f(3x)=2(3x)2=2(9x2)=18x2

Thus, f(3x)=18x2.

3f(x)=3(2x2)=6x2

Hence, 3f(x)=6x2.

Therefore, f(3x)3f(x).

So, the given statement is false.

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