Perform the requested operation or operations. Find the domain of each.
-$$f ( x ) = \sqrt { x } ; g ( x ) = 6 x - 7$$
Find $f / g$.
A) $( \mathrm { f } / \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 6 \mathrm { x } - 7 } ;$ domain $\left\{ x \mid x \geq 0 , x \neq \frac { 7 } { 6 } \right\}$
B) $( f / g ) ( x ) = \frac { 6 x - 7 } { \sqrt { x } } ;$ domain $\{ x \mid x \geq 0 \}$
C) $( \mathrm { f } / \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 6 \mathrm { x } - 7 }$; domain $\{ x \mid x \neq 0 \}$
D) $( \mathrm { f } / \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 6 \mathrm { x } - 7 } ;$ domain $\left\{ x \mid x \neq \frac { 7 } { 6 } \right\}$

Question

Quizplus · Accepted Answer

The division of $f(x)$ by $g(x)$ results in $\frac{\sqrt{x}}{6x-7}$. The domain is all $x \geq 0$ because of the square root in the numerator, and $x \neq \frac{7}{6}$ because $6x-7$ in the denominator cannot be zero.

Perform the Requested Operation or Operations f(x)=x;g(x)=6x−7f ( x ) = \sqrt { x } ; g ( x ) = 6 x - 7f(x)=x​;g(x)=6x−7

Perform the Requested Operation or Operations $f ( x ) = \sqrt { x } ; g ( x ) = 6 x - 7$