f(x) = 3x + 4; g(x)= 5x - 1
Find $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) .$
A) $\left( \frac { f } { g } \right) ( x ) = \frac { 3 x + 4 } { 5 x + 1 } , \text { where } x \neq - \frac { 1 } { 5 }$
B) $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x + 1 } { 3 x + 4 } , \text { where } x \neq - \frac { 4 } { 3 }$
C) $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 1 } { 3 x + 4 } , \text { where } x z - \frac { 4 } { 3 }$
D) $\left( \frac { f } { g } \right) ( x ) = \frac { 3 x + 4 } { 5 x - 1 } , \text { where } x \neq \frac { 1 } { 5 }$

Question

Quizplus · Accepted Answer

The division of two functions $f(x)$ over $g(x)$ is correctly represented in option D, with the correct domain restriction $x \neq \frac{1}{5}$ to avoid division by zero in $g(x)$.

F(x) = 3x + 4; G(x)= 5x - 1 Find (fg)(x).\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) .(gf​)(x).

F(x) = 3x + 4; G(x)= 5x - 1
Find $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) .$