Chapter 1, Problem 8RQ

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

You can always divide by e^x.

To determine

Whether the statement, you can always divide by $e^x$ is true or false.

Answer to Problem 8RQ

Solution:

The statement is true.

Explanation of Solution

Let the function be $f\left(x\right)=e^x$.

Then, the graph of $f\left(x\right)=e^x$ is shown below in Figure 1.

From Figure 1, It is observed that $e^x$ never 0 for any values of x and it has domain $\left(-\infty ,\infty \right)$ and range $\left(0,\infty \right)$.

Thus, divisor $e^x$, always a number.

Since a number can be divided by a number, the given statement is always true.