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:xε

**R**}.

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 x

∈**R**, 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.