# How do you determine the domain of f(x)=1/sqrt(x+2)?

May 8, 2017

$x > - 2$ or:
$\left(- 2 , \infty\right)$

#### Explanation:

$f \left(x\right) = \frac{1}{\sqrt{x + 2}}$

The domain of a function is the set of all the real values of x input for which the function is defined. The domain can also be defined as set of all the real numbers except those that make the function undefined. Now in this case:
$\frac{1}{\sqrt{x + 2}}$
We can't have zero for the denominator nor a negative square root since both will make the function undefined, then:
$x + 2 > 0$ => or:
$x > - 2$ => or:
$\left(- 2 , \infty\right)$