Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 49 }$.
A) $[ - 7,7 ]$
B) $( - 7,0 ] \cup [ 0,7 )$
C) $( - \infty , - 7 ) \cup ( - 7,7 ) \cup ( 7 , \infty )$
D) $( - \infty , - 7 ] \cup [ 7 , \infty )$
E) $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The function $g(x) = \frac{1}{x^2 - 49}$ is undefined when the denominator is zero, which occurs at $x^2 - 49 = 0$, or $x^2 = 49$. Solving for $x$, we get $x = \pm7$. Therefore, the domain excludes $-7$ and $7$, making the correct domain $(-\infty, -7) \cup (-7, 7) \cup (7, \infty)$.

Determine the Domain Of g(x)=1x2−49g ( x ) = \frac { 1 } { x ^ { 2 } - 49 }g(x)=x2−491​

Determine the Domain Of $g ( x ) = \frac { 1 } { x ^ { 2 } - 49 }$