For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2$$
Find $\frac { f } { g }$.
A) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 2 } ; \{ \mathrm { x } \mid \mathrm { x } \neq 0 \}$
B) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 2 } ; \left\{ \mathrm { x } \mid \mathrm { x } \geq 0 , \mathrm { x } \neq \frac { 2 } { 5 } \right\}$
C) $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 2 } ; \left\{ x \mid x \neq \frac { 2 } { 5 } \right\}$
D) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 5 \mathrm { x } - 2 } { \sqrt { \mathrm { x } } } ; \{ \mathrm { x } \mid \mathrm { x } \geq 0 \}$

Question

Quizplus · Accepted Answer

The correct function for $\frac{f}{g}$ is $\frac{\sqrt{x}}{5x-2}$ because you divide $f(x)$ by $g(x)$. The domain is $x \geq 0$ because of the square root in $f(x)$, and $x \neq \frac{2}{5}$ because $5x-2$ cannot be zero (to avoid division by zero).

For the Given Functions F and G, Find the Requested f(x)=x;g(x)=5x−2f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2f(x)=x​;g(x)=5x−2

For the Given Functions F and G, Find the Requested $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2$