Find the domain of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } - 81 } { x ^ { 2 } + 7 x - 18 }$$
A) domain of $f : ( \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$
B) domain of $f : ( \infty , - 9 ) \cup ( - 9,2 ) \cup ( 2 , \infty )$
C) domain of $f : ( \infty , - 2 ) \cup ( - 2,9 ) \cup ( 9 , \infty )$
D) domain of $f : ( \infty , 0 ) \cup ( 0 , \infty )$

Question

Find the domain of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } - 81 } { x ^ { 2 } + 7 x - 18 }$$
A) domain of $f : ( \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$ 
B) domain of $f : ( \infty , - 9 ) \cup ( - 9,2 ) \cup ( 2 , \infty )$ 
C) domain of $f : ( \infty , - 2 ) \cup ( - 2,9 ) \cup ( 9 , \infty )$ 
D) domain of $f : ( \infty , 0 ) \cup ( 0 , \infty )$

Quizplus · Accepted Answer

The domain of $f(x)$ is all real numbers except those that make the denominator equal to zero. Factoring the denominator $x^2 + 7x - 18 = (x + 9)(x - 2)$, we find that the denominator is zero when $x = -9$ or $x = 2$. Therefore, the domain excludes -9 and 2, making option B correct.

Find the Domain of the Rational Function f(x)=x2−81x2+7x−18f ( x ) = \frac { x ^ { 2 } - 81 } { x ^ { 2 } + 7 x - 18 }f(x)=x2+7x−18x2−81​

Find the Domain of the Rational Function $f ( x ) = \frac { x ^ { 2 } - 81 } { x ^ { 2 } + 7 x - 18 }$