It is, however, NOT true that the domain of is the "set of all x such that x is not equal to plus or minus 3". The (natural) domain of a function is the set of all values of x for which the formula can be calculated. There is no problem with x= 3 or -3: f(3)= 0/3= 0 and f(-3)= 0/(-3)= 0. There is a problem with x= 0 because then the denominator is 0 and we cannot divide by 0. The domain of is .
If the the problem were were with f the reciprocal, , then, because , the denominator would be 0 at x= 3 or x= -3 and the domain would be .