# How do you find the domain and range of y = 1/(x^2 - 2)?

Nov 6, 2017

#### Answer:

Domain: x|oo,-sqrt(2))uu(-sqrt(2),sqrt(2))uu(sqrt(2),oo)
Range: $y | \left(- \infty , 0\right) \cup \left(0 , \infty\right)$

#### Explanation:

$y = \frac{1}{{x}^{2} - 2} = \frac{1}{\left(x + \sqrt{2}\right) \left(x - \sqrt{2}\right)}$ . Function is undefined

if denominator is zero.So function is undefined at $x = \sqrt{2}$

and at $x = - \sqrt{2}$. Domain : Any real number of $x$ except

$x = \pm \sqrt{2}$. Domain: $x \in \mathbb{R} | x \ne \pm \sqrt{2}$. In interval notation

expressed as $x | \left(- \infty , - \sqrt{2}\right) \cup \left(- \sqrt{2} , \sqrt{2}\right) \cup \left(\sqrt{2} , \infty\right)$.

Range: Any real number of $y$ except $y = 0$

Range: $y \in \mathbb{R} | y \ne 0$.In interval notation expressed as

$y | \left(- \infty , 0\right) \cup \left(0 , \infty\right)$

graph{1/(x^2-2) [-10, 10, -5, 5]} [Ans]