# How do you find the domain of f(x) = (3x^2)/(x^2-49)?

May 2, 2017

$\text{domain } x \in \mathbb{R} , x \ne \pm 7$

#### Explanation:

The denominator of f(x) cannot be 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.

$\text{solve } {x}^{2} - 49 = 0 \Rightarrow \left(x - 7\right) \left(x + 7\right) = 0$

$\Rightarrow x = - 7 \text{ and " x=7larrcolor(red)" are excluded values}$

$\text{domain } x \in \mathbb{R} , x \ne \pm 7$