Find the specified domain.
-Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = 2 x - 6$ and $g ( x ) = 7 x - 2$
A) $\left( \infty , \frac { 2 } { 7 } \right) \cup \left( \frac { 2 } { 7 } , \infty \right)$
B) $( - \infty , 3 ) \cup ( 3 , \infty )$
C) $( - \infty , \infty )$
D) $\left( \infty , \frac { 2 } { 7 } \right) \cup \left( \frac { 2 } { 7 } , 3 \right) \cup ( 3 , \infty )$

Question

Quizplus · Accepted Answer

The domain of $\left( \frac { f } { g } \right) ( x )$ is all real numbers except where $g(x) = 0$. For $g(x) = 7x - 2$, setting it to zero gives $7x - 2 = 0$, solving for $x$ gives $x = \frac{2}{7}$. Thus, the domain excludes $\frac{2}{7}$, which is represented by $\left( \infty , \frac { 2 } { 7 } \right) \cup \left( \frac { 2 } { 7 } , \infty \right)$.

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

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