Chapter 1 - Section 1.2 - Combining Functions; Shifting and Scaling Graphs - Exercises - Page 19: 19

$g(x)=\frac{2x}{x-1}$

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