Question

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

Answer 1

`x>=-9, x!=-6 and x!=-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:

`(x+6)(x+4)!=0`

So `x!=-6 and x!=-4`

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

`x+9>=0`

So `x>=-9`

Therefore our domain is the set of all numbers greater than or equal to `-9` but not `-6 or -4`

Another way to say that is:

`x>=-9, x!=-6 and x!=-4`