Generally it should be written in math blackboard font, as $x \in \mathbb{R}$ in LaTeX and it will look like $\displaystyle x\in \mathbb{R}$. On these forums you need to wrap in in math tags, like pickslides mentioned.
How would you read the entire first line out loud (labeled (3) )?
In the algebra book I'm using, it uses a colon ":" for "such that", whereas here I think the vertical bar is being used as "such that" in the set notation.
"f sends x to the square root of the quantity x+3, where the domain is: The set of all x such that x is greater than or equal to -3, and x is an element of the real numbers."
| and : are both common notations for such that in sets.