Question

I'm not good at these kinds of questions, please help.

State the domain of the rational function:

f(x) =
x
x2 + 4
A)
(-∞, ∞)
B)
(-∞, 0] ∪ [0, ∞)
C)
(-∞, -2) ∪ (-2, 2) ∪ (2, ∞)
D)
(-∞, -2] ∪ [-2, 2] ∪ [2, ∞)

Answer 1

\[f(x) = \frac{x}{x^2+4}?\]

Answer 2

Is that the f(x)?

Answer 3

Yeah sorry the x/x^2+4 is the f(x)

Answer 4

Domain is all allowed values of x.
Are there any restrictions on x here?
Normally when we have a rational function we want to make sure the denominator does not become zero. Here the denominator is x^2 + 4 which will never become zero for any real value of x because x^2 will always be positive or o and when added to 4 the denom will always be positive.
So no restriction on x. Domain (-infinity, infinity)

Answer 5

Ok, i understand that the denominator does not become zero. And I was about to decide the answer was C. Would that be correct?

Answer 6

I have already given you the answer. Domain is (-infinity, infinity)

Answer 7

Oh Sorry didnt really carefully. Thank you.

Answer 8

yw.