Determine the domain of the function.
-$f ( x ) = \frac { 1 - 2 x } { x ^ { 3 } - 20 x ^ { 2 } + 96 x }$
A) $\left\{ x \mid x \neq 12 , x \neq 8 , x \neq \frac { 1 } { 2 } \text {, and } x \neq 0 \right\}$
B) $\{ x \mid x \neq - 12 , x \neq 8 \text {, and } x \neq 0 \}$
C) $\left\{ x \mid x \neq 12 , x \neq 8 , \text { and } x \neq \frac { 1 } { 2 } \right\}$
D) $\{ x \mid x \neq 12 , x \neq 8 , \text { and } x \neq 0 \}$

Question

Quizplus · Accepted Answer

The domain of the function is determined by the values of $x$ for which the denominator is not equal to zero. Factoring the denominator $x^3 - 20x^2 + 96x = x(x^2 - 20x + 96) = x(x-12)(x-8)$, we find that the denominator is zero when $x = 0$, $x = 12$, or $x = 8$. Therefore, these values must be excluded from the domain. The numerator does not introduce any additional restrictions on the domain.

Determine the Domain of the Function f(x)=1−2xx3−20x2+96xf ( x ) = \frac { 1 - 2 x } { x ^ { 3 } - 20 x ^ { 2 } + 96 x }f(x)=x3−20x2+96x1−2x​

Determine the Domain of the Function $f ( x ) = \frac { 1 - 2 x } { x ^ { 3 } - 20 x ^ { 2 } + 96 x }$