Let $f ( x ) = 5 x - 9$ and $g ( x ) = 4 x - 2$ . Find the domain of $\frac { f } { g }$ .
A) $( - \infty , 0 ) \cup ( 0 , \infty )$
B) $( - \infty , \infty )$
C) $\left( - \infty , \frac { 9 } { 5 } \right) \cup \left( \frac { 9 } { 5 } , \infty \right)$
D) $\left( - \infty , \frac { 1 } { 2 } \right) \cup \left( \frac { 1 } { 2 } , \infty \right)$

Question

Quizplus · Accepted Answer

The domain of $\frac{f}{g}$ is all real numbers except where $g(x) = 0$. Solving $4x - 2 = 0$ gives $x = \frac{1}{2}$, so the domain excludes $\frac{1}{2}$, leading to the answer $\left( - \infty , \frac { 1 } { 2 } \right) \cup \left( \frac { 1 } { 2 } , \infty \right)$.

Let f(x)=5x−9f ( x ) = 5 x - 9f(x)=5x−9 And g(x)=4x−2g ( x ) = 4 x - 2g(x)=4x−2

Let $f ( x ) = 5 x - 9$ And $g ( x ) = 4 x - 2$