Find the domain of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } - 8 x + 12 }$$
A) domain of $f : ( \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$
B) domain of $f : ( \infty , 0 ) \cup ( 0 , \infty )$
C) domain of $f : ( \infty , 2 ) \cup ( 2,6 ) \cup ( 6 , \infty )$
D) domain of $f : ( \infty , - 6 ) \cup ( - 6 , - 2 ) \cup ( - 2 , \infty )$

Question

Find the domain of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } - 8 x + 12 }$$
A) domain of $f : ( \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
B) domain of $f : ( \infty , 0 ) \cup ( 0 , \infty )$ 
C) domain of $f : ( \infty , 2 ) \cup ( 2,6 ) \cup ( 6 , \infty )$ 
D) domain of $f : ( \infty , - 6 ) \cup ( - 6 , - 2 ) \cup ( - 2 , \infty )$

Quizplus · Accepted Answer

The domain of $f(x)$ is determined by the values of $x$ for which the denominator $x^2 - 8x + 12$ is not equal to zero. Factoring the denominator gives $(x-2)(x-6)$, which means the denominator is zero at $x=2$ and $x=6$. Therefore, the domain excludes $x=2$ and $x=6$, making the correct domain $(-\infty, 2) \cup (2, 6) \cup (6, \infty)$.

Find the Domain of the Rational Function f(x)=x2−9x2−8x+12f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } - 8 x + 12 }f(x)=x2−8x+12x2−9​

Find the Domain of the Rational Function $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } - 8 x + 12 }$