Find the domain of the function.
-$$h ( x ) = \frac { x - 2 } { x ^ { 3 } - 9 x }$$
A) $\{ x \mid x \neq 2 \}$
B) $\{ x \mid x \neq 0 \}$
C) all real numbers
D) $\{ x \mid x \neq - 3,0,3 \}$

Question

Quizplus · Accepted Answer

The domain of the function $h(x) = \frac{x - 2}{x^3 - 9x}$ is determined by the values of $x$ for which the denominator is not equal to zero. Factoring the denominator gives $x(x^2 - 9) = x(x - 3)(x + 3)$. Thus, the denominator is zero when $x = 0$, $x = 3$, or $x = -3$. Therefore, the domain excludes these values, making the correct answer $\{ x \mid x \neq -3, 0, 3 \}$.

Find the Domain of the Function h(x)=x−2x3−9xh ( x ) = \frac { x - 2 } { x ^ { 3 } - 9 x }h(x)=x3−9xx−2​

Find the Domain of the Function $h ( x ) = \frac { x - 2 } { x ^ { 3 } - 9 x }$