Find the domain of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 x + 14 }$$
A) domain of $f : ( \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$
B) domain of $f : ( \infty , 2 ) \cup ( 2,7 ) \cup ( 7 , \infty )$
C) domain of $f : ( \infty , - 7 ) \cup ( - 7 , - 2 ) \cup ( - 2 , \infty )$
D) domain of $f : ( \infty , 0 ) \cup ( 0 , \infty )$

Question

Find the domain of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 x + 14 }$$
A) domain of $f : ( \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
B) domain of $f : ( \infty , 2 ) \cup ( 2,7 ) \cup ( 7 , \infty )$ 
C) domain of $f : ( \infty , - 7 ) \cup ( - 7 , - 2 ) \cup ( - 2 , \infty )$ 
D) domain of $f : ( \infty , 0 ) \cup ( 0 , \infty )$

Quizplus · Accepted Answer

The domain of a function is the set of all possible inputs (x-values) for which the function is defined. For the function $f(x) = \frac{x^2 - 9}{x^2 + 9x + 14}$, the only restrictions on the domain come from the denominator, since division by zero is undefined. The denominator is $x^2 + 9x + 14$, which can be factored as $(x + 7)(x + 2)$. Therefore, the function is undefined when $x = -7$ or $x = -2$, leading to the domain being all real numbers except $x = -7$ and $x = -2$, which matches choice C: $(-\infty, -7) \cup (-7, -2) \cup (-2, \infty)$.

Find the Domain of the Rational Function f(x)=x2−9x2+9x+14f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 x + 14 }f(x)=x2+9x+14x2−9​

Find the Domain of the Rational Function $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 x + 14 }$