State the domain of the rational function.
-$$f ( x ) = \frac { ( x - 8 ) ( x + 6 ) } { x ^ { 2 } - 4 }$$
A) $( - \infty , \infty )$
B) $( - \infty , - 6 ) \cup ( - 6,8 ) \cup ( 8 , \infty )$
C) $( - \infty , - 2 ) \cup ( - 2,2 ) \cup ( 2 , \infty )$
D) $( - \infty , - 8 ) \cup ( - 8,6 ) \cup ( 6 , \infty )$

Question

Quizplus · Accepted Answer

The domain of a rational function is all real numbers except where the denominator is zero. The denominator $x^2 - 4$ factors to $(x - 2)(x + 2)$, so the function is undefined at $x = 2$ and $x = -2$, making the correct domain $( - \infty , - 2 ) \cup ( - 2,2 ) \cup ( 2 , \infty )$.

State the Domain of the Rational Function f(x)=(x−8)(x+6)x2−4f ( x ) = \frac { ( x - 8 ) ( x + 6 ) } { x ^ { 2 } - 4 }f(x)=x2−4(x−8)(x+6)​

State the Domain of the Rational Function $f ( x ) = \frac { ( x - 8 ) ( x + 6 ) } { x ^ { 2 } - 4 }$