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

1 Answer
Oct 20, 2017

Answer:

#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#