Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }$.
A) $[ - 9,9 ]$
B) $( - 9,0 ] \cup [ 0,9 )$
C) $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$
D) $( - \infty , - 9 ] \cup [ 9 , \infty )$
E) $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The denominator $x^2 - 81$ cannot be zero, as division by zero is undefined. Factoring the denominator gives $(x + 9)(x - 9)$, which is zero at $x = 9$ and $x = -9$. Therefore, the domain excludes -9 and 9, making the correct domain $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$.

Determine the Domain Of g(x)=1x2−81g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }g(x)=x2−811​

Determine the Domain Of $g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }$