# How do you find the domain of f(x)= (x^2-16) / (2x^2+13x+6)?

##### 1 Answer
Jul 8, 2015

Domain is x in RR-{-6;-1/2}

#### Explanation:

The domain is the largest subset of $\mathbb{R}$ for which all the operations in function are defined. In this example the only restriction is that the denominator must be different from zero, so we have to find the zeros of $2 {x}^{2} + 13 x + 6$.

$2 {x}^{2} + 13 x + 6 = 0$

$\Delta = {13}^{2} - 4 \cdot 2 \cdot 6$
$\Delta = 169 - 48 = 121$
$\sqrt{\Delta} = 11$

${x}_{1} = \frac{- 13 - 11}{4} = - 6$

${x}_{2} = \frac{- 13 + 11}{4} = - \frac{1}{2}$

Finally we can write the answer:
Domain is: x in RR-{-6;-1/2}