Question

Determine a função inversa $\frac{f(x)}{} \frac{x}{x-2}$

Answer 1

$f(x)= \dfrac{x}{x-2}\\\\ f(x)=y\\\\ y= \dfrac{x}{x-2}\\\\ troca~x~por~y..\\\\ x= \dfrac{y}{y-2}\\\\ x\cdot (y-2)=y\\ xy-2x=y\\ -2x=y -xy\\ -2x=y(1-x)\\\\ y= \dfrac{-2x}{1-x} \\\\ y= -\dfrac{2x}{1-x}~~(multiplica~por~-1)\\\\ y= \dfrac{2x}{x-1}\\\\\\ \Large\boxed{f^{-1}(x)= \dfrac{2x}{x-1}}$