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## Homework Statement

Find the inverse of a rational function: [itex]f(x)=\frac{2x}{x-2}[/itex]

## The Attempt at a Solution

1. Verify the function is one-to-one.

Question: is there a way to do that withought drawing the graph? Some algebraic method? I know that this means that the function crosess any given x=a line only once, so, e.g. the function with two y intercepts would not be 1-1 ???

2. show that [itex]f(x)=f^{-1}(x)[/itex]

Q.: How to express the given equation in the form where x is given in terms of y? It is imposible since you always get either y or x on both sides.