Answer
$\text{odd}$
Work Step by Step
Recall:
a) A function is said to be odd, when every number $x$ in its domain, the number $-x$ is also in the domain such that $h(-x)=-h(x)$
b) A function is said to be even, when every number $x$ in its domain, the number $-x$ is also in the domain such that $h(-x)=h(x)$
Replace $x$ with $-x$ to evaluate $h(-x)$:
$h(-x)=\dfrac{-(-x)^3}{3(-x)^2-9} \\=\dfrac{-(-x^3)}{3x^2-9}\\=-\dfrac{-x^3}{3x^2-9} \\=-h(x)$
Therefore, the function $h(x)$ is odd.
