Find the domain of the rational function.
-$$g ( x ) = \frac { x } { x ^ { 3 } - 216 }$$
A) $\{ x \mid x \neq 6 \}$
B) $\{ x | x \neq - 6 \rangle$
C) $\{ x | x \neq - 6,6 \rangle$
D) $\{ x \mid x \neq 36 \}$

Question

Quizplus · Accepted Answer

The domain of a rational function includes all real numbers except those that make the denominator equal to zero. To find the values that are not in the domain, set the denominator equal to zero and solve for $x$: $x^3 - 216 = 0$. Factoring, we get $x^3 = 216$, which gives $x = 6$ (since $6^3 = 216$). Therefore, the only value not in the domain is $x = 6$, making the correct choice $\{ x \mid x \neq 6 \}$.

Find the Domain of the Rational Function g(x)=xx3−216g ( x ) = \frac { x } { x ^ { 3 } - 216 }g(x)=x3−216x​

Find the Domain of the Rational Function $g ( x ) = \frac { x } { x ^ { 3 } - 216 }$