Chapter 1, Problem 2RQ

To determine

Whether the statement, if $f\left(s\right)=f\left(t\right)$, then s = t is true or false.

Answer to Problem 2RQ

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 $f\left(x\right)=\frac{x^2}{4}$.

Consider the value of $s=1\text{ and }t=-1$.

Obtain the value of $f\left(s\right)\text{ and }f\left(t\right)$ by substituting the respective values of s and t.

$\begin{array}{c}f\left(s\right)=\frac{1^2}{4}\\ =\frac{1}{4}\\ f\left(t\right)=\frac{{\left(-1\right)}^2}{4}\\ =\frac{1}{4}\end{array}$

Hence, $f\left(s\right)=f\left(t\right)$ but $s\ne t$.

Therefore, the given statement is false.