Solve the problem.
-$\text { Given } f ( x ) = \frac { 1 } { x } \text { and } \left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x } \text {, find the function } g \text {. }$
A) $g ( x ) = \frac { x + 4 } { x + 6 }$
B) $g ( x ) = \frac { x + 6 } { x + 4 }$
C) $g ( x ) = \frac { x - 4 } { x - 6 }$
D) $g ( x ) = \frac { x - 6 } { x - 4 }$

Question

Quizplus · Accepted Answer

Given $\left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x }$ and $f(x) = \frac{1}{x}$, we find $g(x)$ by rearranging the equation: $g(x) = \frac{f(x)}{\left( \frac { f } { g } \right) ( x )}$. Substituting $f(x) = \frac{1}{x}$ and $\left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x }$, we get $g(x) = \frac{x(x^2 - 6x)}{x-4}$. Simplifying, $g(x) = \frac{x^2 - 6x}{x-4}$, which can be further simplified to $g(x) = \frac{x(x - 6)}{x-4}$, matching choice D.

Solve the Problem A) g(x)=x+4x+6g ( x ) = \frac { x + 4 } { x + 6 }g(x)=x+6x+4​

Solve the Problem A) $g ( x ) = \frac { x + 4 } { x + 6 }$