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)
