Whether the statement, if f ( s ) = f ( t ) , then s = 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 2RQ
To determine

Whether the statement, if f(s)=f(t), then s = 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)=x24.

Consider the value of s=1 and t=1.

Obtain the value of f(s) and  f(t) by substituting the respective values of s and t.

f(s)=124=14f(t)=(1)24=14

Hence, f(s)=f(t) but st.

Therefore, the given statement is false.

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