Find the specified domain and express it in interval notation.
-For $f ( x ) = x ^ { 2 } - 81$ and $g ( x ) = 2 x + 3$, what is the domain of $\left( \frac { g } { f } \right) ( x )$ ?
A) $\left[ - \frac { 3 } { 2 } , \infty \right)$
B) All real numbers
C) $\left( - \infty , \frac { 3 } { 2 } \right) \cup \left( - \frac { 3 } { 2 } , \infty \right)$
D) $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$

Question

Quizplus · Accepted Answer

The domain of $\left( \frac { g } { f } \right) ( x )$ excludes values where the denominator $f(x) = x^2 - 81$ equals zero, which occurs at $x = 9$ and $x = -9$. Thus, the domain is all real numbers except $x = 9$ and $x = -9$, represented as $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$.

Find the Specified Domain and Express It in Interval Notation f(x)=x2−81f ( x ) = x ^ { 2 } - 81f(x)=x2−81

Find the Specified Domain and Express It in Interval Notation $f ( x ) = x ^ { 2 } - 81$