The domain of a function is all the values that x can safely be replaced with.
There is something missing from this function.
It should be f(x) = -x^4 + x^3 + 9x or y = -x^4 +x^3 + 9x.
Otherwise, all you have is a polynomial but no function.
In any case, for this question, x can be any number you like.
So, the domain is ALL REAL NUMBERS.