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.