Chapter 2, Problem 6RE

In Problems 6-11, find the domain of each function.

$f\left(x\right)\text{ = }\frac{x}{x^2-9}$

To determine

To find: The domain of the provided function.

Answer to Problem 6RE

Solution:

The domain of the function $f$ is $\left\{x\right|x\ne -3,x\ne 3$.

Explanation of Solution

Given:

It is provided in the problem that the function is $f\left(x\right)=\frac{x}{x^2-9}$.

Formula used:

Rules used to find the domain of a function defined by an equation:

1. Start with the domain as the set of all numbers.

2. If the equation has a denominator, exclude any numbers that give a zero denominator.

3. If the equation has a radical of even index, exclude any numbers that cause the expression inside the radical (the radicand) to be negative.

The function $f$ says to divide $x$ by $x^2-9$. Since division by 0 is not defined, the denominator $x^2-9$ can never be 0, so $x$ can never equal $-3$ or 3. The domain of the function $f$ is $\left\{x\right|x\ne -3,x\ne 3\}$.