f(x) = x³ - 2

This calls for cubing and subtacting.

All valuex of x can be cubed and then have 2 subtracted 
from the result.  So the domain is "all real numbers" or
ℛ or (-∞,∞)

Only division and even roots can keep the domain of a rational
functions from including all real numbers.  The only basic
operations that cannot be done in real number mathematics is 
"division by zero" and "taking an even root of a negative 
number". 

Edwin