find the domain of -4sin(3x)
Do you understand what is meant by the word domain of a function? It is the set of valid inputs to that function. For example, the domain of is the set of non-negative numbers.
Now, as papex has said, , and therefore and , are defined for all values of . In other words, the domain of these functions is the set of all real numbers.
There are various ways of writing this set. One is to use the symbol . Another is to use interval notation: .