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

1 Answer
Oct 20, 2017

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