Say we have the function $y=\frac{1}{\sqrt{x^2-3}}$ and we are asked to find the domain.
So basically the function will be undefined when $x = 0$, and is between $-\sqrt{3}$ and $0$ and also, $0$ and $\sqrt{3}$. What would be the best way to express the function's domain?
Could you say something like,
$x:x\neq(-\sqrt{3}, 0 ] $ $\cup$ $[0, \sqrt{3})$
Or is that not mathematically correct?
I feel this is simpler $$x \in (-\infty, -\sqrt{3}) \cup (\sqrt{3}, \infty)$$
$$f(x) : (-\infty, -\sqrt{3}) \cup (\sqrt{3}, \infty) \to (0, \infty)$$