Math Help - Intervals of Continuity

1. f(x) = (x+2)/(x^2 -4)

2. f(x) = (2x+1)/(sqrt x+4)

So if I'm doing this right, then I got (-inf,2] for the first one, and [-4,inf) for the second. But, that's just looking at a graph. So now how would you find these answers (if they are correct that is) by not looking on a graph. Is there some algebraic way of doing this? My textbook isn't helping me much with this kind of question.

Also as a side question; am I doing the interval notation correctly?

Originally Posted by nautica17

1. f(x) = (x+2)/(x^2 -4)

2. f(x) = (2x+1)/(sqrt x+4)

For continuity the function must be definded.

Originally Posted by Plato

For continuity the function must be definded.

But see how do you know that? Is it just something that after a while you know when you see it? I know that polynomials are always continuous, but rational functions, do you just plug some numbers in? I know this is probably a silly problem, but I've always had troubles understanding things related to domains.

Please note the correction in part b.