Question

What is the inverse function of f(x)= x/x-2?​

Answer 1

Answer:

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

Step-by-step explanation:

Start by replacing f(x) by the variable "y" and solving for x in the equation:

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

Now do the final replacement using the inverse function notation, and replacing "y" with "x":

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