The domain is the set of #x# values that are defined for the function #f(x)#.
Naturally a continuous function will have a domain #x in (-oo, +oo)#. However, some functions have discontinuities. These are values of #x# for which the function is not properly defined.
With rational functions, these invalid #x# values occur when the denominator is #0#, as division by zero is undefined.
We have #x-3 = 0-> x = 3# as a value of #x# that our function cannot take. We write this new domain as a combination of domains extending to infinity and containing all #x# values as close to #3# as possible without including #3# itself:
#x in (-oo, 3) cup (3, +oo)#
