Find the domain of the function

Question

Find the domain of the function. (Enter your answer using interval notation.)
f(x) = x + 4/x^2 − 36

 

How would I go about solving this?

 

Thanks

Answer 1

You need to group terms in parentheses.  I assume you meant to say

 

f(x) = (x + 4) / (x² - 36)

 

Factor the denominator to find where it is zero.

 

f(x) = (x + 4) / [(x - 6)(x + 6)]

 

The domain is all real numbers except x = ±6

 

Answer 2

The domain of every rational algebraic function has exclusions, which are zeros of the complete denominator.

Both the numerator & the denominator of your problem require their own individual parentheses, because you do not have a long horizontal division symbol as you would be able to use if writing on paper.

 

The domain is all reals except ±6