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

B) $g ( x ) = \frac { x + 6 } { x + 4 }$

C) $ g ( x ) = \frac { x - 4 } { x - 6 }$

D) $g ( x ) = \frac { x + 4 } { x + 6 }$

Question

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

B) $g ( x ) = \frac { x + 6 } { x + 4 }$

C) $  g ( x ) = \frac { x - 4 } { x - 6 }$

D) $g ( x ) = \frac { x + 4 } { x + 6 }$

Quizplus · Accepted Answer

Given $\left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x }$ and $f ( x ) = \frac { 1 } { x }$, we can substitute $f(x)$ into the equation to solve for $g(x)$. This gives us $\frac { \frac{1}{x} } { g(x) } = \frac { x - 4 } { x ^ { 2 } - 6 x }$. Simplifying, we find $g(x) = \frac{x}{x-4} \cdot \frac{x^2-6x}{1}$, which simplifies further to $g(x) = \frac{x(x-6)}{x-4}$, or $g(x) = \frac{x-6}{x-4}$, matching choice A.

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