For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation.
-$f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2 ; \quad$ Find $\frac { r } { g }$.
A) $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 2 } ; \left( * , \frac { 2 } { 5 } \right) \cup \left( \frac { 2 } { 5 } , \infty \right)$
B) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 2 } ; \left( 0 , \frac { 2 } { 5 } \right) \cup \left( \frac { 2 } { 5 } , \infty \right)$
C) $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 2 } ; ( \infty , 0 ) \cup ( 0 , \infty )$
D) $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 2 } { \sqrt { x } } ; [ 0 , \infty )$

Question

Quizplus · Accepted Answer

The function $\frac{f}{g}(x) = \frac{\sqrt{x}}{5x - 2}$ is defined for $x > 0$ because of the square root in the numerator, and $x \neq \frac{2}{5}$ because the denominator cannot be zero. Therefore, the domain is $(0, \frac{2}{5}) \cup (\frac{2}{5}, \infty)$.

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

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