It means "not equal".

ragequitter, you should take a gander at

Online LaTeX Equation Editor
and add a little Latex markup to your posts.

$\displaystyle \neq$ is achieved by "\neq" between tex tags.

There is a general way for determining the domain of real-valued functions such as the ones you listed.

1. Start with all real numbers.

2. Exclude any values that would lead to zero in the denominator, or a negative under an even radical (including square roots, 4th roots, etc). logarithms must have positive arguments also, but we're looking at rational functions (adjoin sqrt) for the moment.

$\displaystyle y=\frac{9x^2}{25-x^2}$

The bottom cannot be zero, so solve

$\displaystyle 25 - x^2 \neq 0$ to get

$\displaystyle x \neq \pm 5$

That. Is. It! Sure, you can write that in interval notation, but the result is the same.

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For the range, it's not as cut-and-dry. You can't always solve for x. More advanced techniques might come into play.

It's a shame that you aren't familiar (comfortable) with end behavior (i.e. "limits at infinity") and the like.

Have you heard about even/odd functions? You can use symmetry in the case of y as given above.

You can use partial fraction decomposition... actually, that might be best in this case. I suspect the range is (almost?) every real number.