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find the domain of the raional function

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2 Answers

 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,∞)



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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."