# What is the domain and range of  f(x) = 5/ |x|-3 ?

Dec 9, 2015

Domain $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

Range : $\left(- 3 , + \infty\right)$

#### Explanation:

Domain: Set of possible x values of the given function.

We have x in the denominator , so we could not take $x = 0$

so we can take any real number except 0 , for the domain.

Range : set of possible y value.

$y = \frac{5}{\left\mid x \right\mid} - 3$

$y + 3 = \frac{5}{\left\mid x \right\mid}$

$\frac{5}{\left\mid x \right\mid} > 0$ ,AA x; since $\left\mid x \right\mid > 0 \forall x$.

$y + 3 > 0$

so $y > - 3$