# Whether the statement, if f is a function, then f ( s + t ) = f ( s ) + f ( t ) 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 1RQ
To determine

## Whether the statement, if f is a function, then f(s+t)=f(s)+f(t) 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.

Consider the value of s=1 and t=1.

Find the value of f(s+t),f(s) and f(t) by substituting the respective s and t values.

f(s+t)=f(1+(1))=f(0)=0

Thus, f(s+t)=0

f(s)=2(1)2=2f(t)=2(1)2=2

Hence, f(s)+f(t)=4

Therefore, f(s+t)f(s)+f(t).

So, the given statement is false.

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