find the domain of -4sin(3x)
Hello winsome
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 $\displaystyle \sqrt x$ is the set of non-negative numbers.
Now, as papex has said, $\displaystyle \sin x$, and therefore $\displaystyle \sin3x$ and $\displaystyle -4\sin 3x$, are defined for all values of $\displaystyle x$. 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 $\displaystyle \mathbb{R}$. Another is to use interval notation: $\displaystyle (-\infty, +\infty)$.
Grandad