Find the specified domain.
-Find the domain of $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } )$ when $\mathrm { f } ( \mathrm { x } ) = 2 \mathrm { x } - 5$ and $g ( x ) = \frac { 2 } { \mathrm { x } - 7 }$
A) $( - \infty , \infty )$
B) $\left( - \infty , \frac { 5 } { 2 } \right) \cup \left( \frac { 5 } { 2 } , 7 \right) \cup ( 7 , \infty )$
C) $( - \infty , 7 ) \cup ( 7 , \infty )$
D) $( - \infty , - 7 ) \cup ( - 7 , \infty )$

Question

Quizplus · Accepted Answer

The domain of $g(x) = \frac{2}{x-7}$ excludes $x = 7$ because division by zero is undefined. The function $f(x) = 2x - 5$ has a domain of all real numbers. When dividing $f(x)$ by $g(x)$, the only restriction comes from $g(x)$, thus the domain is all real numbers except $x = 7$.

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

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