Find the specified domain.
-Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = 9 x - 5$ and $g ( x ) = \frac { 2 } { x - 11 }$
A) $\left( \infty , \frac { 5 } { 9 } \right) \cup \left( \frac { 5 } { 9 } , 11 \right) \cup ( 11 , \infty )$
B) $( - \infty , - 11 ) \cup ( - 11 , \infty )$
C) $( - \infty , 11 ) \cup ( 11 , \infty )$
D) $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The domain of $\left( \frac { f } { g } \right) ( x )$ excludes values that make the denominator zero. Since $g(x) = \frac{2}{x-11}$, the denominator is zero when $x = 11$. Therefore, the domain is all real numbers except $x = 11$, which is option C: $( - \infty , 11 ) \cup ( 11 , \infty )$.

Find the Specified Domain (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x)

Find the Specified Domain $\left( \frac { f } { g } \right) ( x )$