Question

Determine a funcão inversa f^-1(x) da funcão F:R-{2}⇒R-{1} dada por f(x)= $\frac{x}{x-2}$

Answer 1

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