BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 1RQ

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!