Answer
Neither even nor odd
Work Step by Step
If $f(-x)=f(x)$ then the function is even.
If $f(-x)=-f(x)$ then the function is odd.
If $f(-x)\neq f(x)$ and $f(-x)\neq -f(x)$ then the function is neither odd nor even.
$$f(x)=x^3-x+9$$ $$f(-x)=(-x)^3-(-x)+9=-x^3+x+9=-(x^3-x-9)$$
It is neither $f(x)$ nor $-f(x)$, so, neither even nor odd.
