For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 8$
Find $\frac { \mathrm { f } } { \mathrm { g } }$.
A) $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 8 } { \sqrt { x } } ; \{ x \mid x \geq 0 \}$
B) $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 8 } ; \left\{ x \mid x \geq 0 , x \neq \frac { 8 } { 5 } \right\}$
C) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 8 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 8 } { 5 } \right\}$
D) $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 8 } ; \{ x \mid x \neq 0 \}$

Question

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 8$
Find $\frac { \mathrm { f } } { \mathrm { g } }$. 
A) $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 8 } { \sqrt { x } } ; \{ x \mid x \geq 0 \}$
B) $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 8 } ; \left\{ x \mid x \geq 0 , x \neq \frac { 8 } { 5 } \right\}$
C) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 8 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 8 } { 5 } \right\}$
D) $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 8 } ; \{ x \mid x \neq 0 \}$

Quizplus · Accepted Answer

The division of $f$ by $g$ gives $\frac{\sqrt{x}}{5x-8}$. The domain includes $x \geq 0$ because of the square root in the numerator, and excludes $x = \frac{8}{5}$ because it makes the denominator zero.

For the Given Functions F and G, Find the Requested f(x)=x;g(x)=5x−8f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 8f(x)=x​;g(x)=5x−8

For the Given Functions F and G, Find the Requested $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 8$