Find the domain of the rational function.
-$$f ( x ) = \frac { x ( x - 1 ) } { 16 x ^ { 2 } + 24 x + 5 }$$
A) $\left\{ x \mid x \neq - \frac { 1 } { 16 } , - \frac { 5 } { 16 } \right\}$
B) $\left\{ x \mid x \neq - \frac { 1 } { 4 } , - \frac { 5 } { 4 } \right\}$
C) $\left\{ x \mid x \neq \frac { 1 } { 4 } , \frac { 5 } { 4 } \right\}$
D) $\left\{ x \mid x \neq - \frac { 5 } { 8 } , \frac { 5 } { 8 } \right\}$

Question

Quizplus · Accepted Answer

The domain of a rational function is all real numbers except where the denominator is zero. To find these values, set the denominator equal to zero and solve for $x$: $16x^2 + 24x + 5 = 0$. Factoring or using the quadratic formula, we find the roots to be $x = -\frac{1}{4}$ and $x = -\frac{5}{4}$. Therefore, the domain excludes these values, matching choice B.

Find the Domain of the Rational Function f(x)=x(x−1)16x2+24x+5f ( x ) = \frac { x ( x - 1 ) } { 16 x ^ { 2 } + 24 x + 5 }f(x)=16x2+24x+5x(x−1)​

Find the Domain of the Rational Function $f ( x ) = \frac { x ( x - 1 ) } { 16 x ^ { 2 } + 24 x + 5 }$