# How do you find the domain of f(x)=sqrt (x+9)/((x+6)(x+4))?

Oct 20, 2017

$x \ge - 9 , x \ne - 6 \mathmr{and} x \ne - 4$

#### Explanation:

The domain is the set of all possible x-values we can plug in to this function.

There are two things that we have to consider when thinking of x-values we cannot plug in to the function:

First we cannot divide by $0$. Thus:

$\left(x + 6\right) \left(x + 4\right) \ne 0$

So $x \ne - 6 \mathmr{and} x \ne - 4$

Second we cannot take the square root of a negative number. Thus:

$x + 9 \ge 0$

So $x \ge - 9$

Therefore our domain is the set of all numbers greater than or equal to $- 9$ but not $- 6 \mathmr{and} - 4$

Another way to say that is:

$x \ge - 9 , x \ne - 6 \mathmr{and} x \ne - 4$