0

# find the domain of the raional function

C(x)= 1/x^2-4

the domain is

### 2 Answers by Expert Tutors

Shannon H. | Mathematics and Science TutorMathematics and Science Tutor
4.9 4.9 (347 lesson ratings) (347)
1
Hi Bridget,  set the the denominator of
x^2-4 0
+4  +4
x^2 ≠ 4
sqrt(x^2) ≠ sqrt(4)
x = ±2
So, the domain of the function will be
{x|x ≠ -2, x ≠ 2} and in interval notation (-∞,-2)U(-2,2)U(2,∞)

so how would I write that into an answer??

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
1
Hi Bridget;
C(x)= 1/x^2-4
I believe this is...
C(x)=1/(x2-4)
You probably already know that a numerator cannot equal zero.
So let's work with 0≠x2-4
Let's factor...
0≠(x-2)(x+2)
Let's separate...
0≠x-2 and 0≠x+2
x≠2  and 0≠-2

The domain is all integers except -2 and 2.
(-infinity,-2)U(-2,2)U(2, +infinity)

According to Michael F., the Wyant of Wilton, CT, "the parentheses ( and ) indicate no endpoints. The symbol ∪ means set union."