Answer:
Domain: the set of all real numbers except -3, 0 and 3.
[tex]\huge\boxed{x\in\mathbb{R}-\{-3,\ 0,\ 3\}}[/tex]
Step-by-step explanation:
[tex]f(x)=\dfrac{2}{x^3-9x}[/tex]
We know that division by 0 is not possible.
The denominator of a fraction must be different 0.
Therefore:
[tex]x^3-9x\neq0\qquad\text{distribute}\\\\x(x^2-9)\neq0\iff \boxed{x\neq0}\ \wedge\ x^2-9\neq0\\\\x^2-9\neq0\qquad\text{add 9 to both sides}\\x^2-9+9\neq0+9\\x^2\neq9\Rightarrow x\neq\pm\sqrt9\\\boxed{x\neq-3\ \wedge\ x\neq3}[/tex]
