to check whether a function is odd or even, we simply substitute the argument by its negative version, namely "x" by "-x".
if the expression simplifies to resemble the original expression, that simply means the expression is even. If it resembles the original negative expression, is odd.
[tex]\bf g(x)=-2x^3-9\\\\
-------------------------------\\\\
\stackrel{x=-x}{g(-x)}=-2(-x)^3-9\implies g(-x)=-2(-x)(-x)(-x)-9
\\\\\\
g(-x)=+2(x)(x)(x)-9\implies g(-x)=2x^3-9[/tex]
well, that doesn't look like the original - 2x³ - 9, so is not even.
and -f(x) would be 2x³ + 9, and that doesn't look like either, so is not odd.
thus is neither.
