## University Calculus: Early Transcendentals (3rd Edition)

$g(x)=\frac{2x}{x-1}$
$f(x)=\frac{x}{x-2}$ $(f\circ g)(x)=x$ $g(x)=?$ Let's say $\ g(x)=y\$, so that the composition of the two functions is represented as: $(f\circ g)(x)=f(g(x))$ $f(y)=\frac{y}{y-2}$ $x=\frac{y}{y-2}$ $yx-2x=y$ $y(x-1)=2x$ $y=\frac{2x}{x-1}$ $g(x)=\frac{2x}{x-1}$