# How do you find the domain of f(x)=(2x^2)/(x^2-9)?

May 20, 2017

$x \in \mathbb{R} , x \ne \pm 3$

#### Explanation:

The domain is defined for all values of x except values that make the denominator of f(x) equal to zero as this would make f(x) $\textcolor{b l u e}{\text{undefined}}$ Equating the denominator to zero and solving gives the values that x cannot be.

$\text{solve } {x}^{2} - 9 = 0 \Rightarrow \left(x - 3\right) \left(x + 3\right) = 0$

$\Rightarrow x = \pm 3 \leftarrow \textcolor{red}{\text{ excluded values}}$

$\Rightarrow \text{domain is } x \in \mathbb{R} , x \ne \pm 3$