First, let’s
plot f(x) =
Here’s what the
graph looks like:
Now, the
definition of “domain of a function” is as follows: The domain of a given
function is the set of "input" values for which the function is
defined.” For instance, the domain of cosine would be all real numbers, while
the domain of the square root would be only numbers greater than or equal to 0
(ignoring complex numbers in both cases).
As you can see
from the above graph, the function is valid for all “real” values of x, except
for 0. The set of “real numbers”, as you may know, can be thought of as points
on an infinitely long number line. The shorthand way of saying “all real
numbers except for x” is as follows: