More generally:

For any function f(x), the domain of f(x) is the set of all inputs that f(x) can take without barfing.

Consider the function f(x) = 2x+3. Now, are there any numbers we can put into this function such that f(x) will be nonreal or undefined? No. So we say that the domain of f(x) is all real numbers, or, in set notation, {x:xεR}.

Now consider the function g(x) = 5/(x+2). For what values of x will g(x) be undefined? Only -2. So the domain of g(x) is all real numbers except for -2, or {x:x!=-2}. (If the domain is anything more complex than xR, then x being a real number is implied.)

For our final example, let h(x) = sqrt(x-3). If x is less than three, then our function will return a nonreal answer, which (at least in high school math) is bad. So, for h(x) to return a real answer, x must be greater than or equal to 3: {x:x>=3}.

Compare range.

/msg me if any of the math symbols don't display right.