Solve the problem.
-Let $f ( x ) = \frac { x } { x - 4 }$. Find a function $y = g ( x )$ so that $( f \circ g ) ( x ) = x$.
A) $g ( x ) = x ( x - 4 )$
B) $g ( x ) = \frac { 1 } { x - 4 }$
C) $g ( x ) = \frac { x - 4 } { 4 }$
D) $g ( x ) = \frac { 4 x } { x - 1 }$

Question

Quizplus · Accepted Answer

To find $g(x)$ such that $(f \circ g)(x) = x$, we need $f(g(x)) = x$. Substituting $g(x) = \frac{4x}{x-1}$ into $f(x)$, we get $f\left(\frac{4x}{x-1}\right) = \frac{\frac{4x}{x-1}}{\frac{4x}{x-1} - 4} = x$, which satisfies the condition.

Solve the Problem f(x)=xx−4f ( x ) = \frac { x } { x - 4 }f(x)=x−4x​

Solve the Problem $f ( x ) = \frac { x } { x - 4 }$