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The inverse function is the function that "undoes".

We can find the inverse function by setting f(x) as y and solving for x in terms of y.

$y(2x-1)=x$

$2xy-y=x$

$y = 2xy-x$

$y=x(2y-1)$

$x=\frac{y}{2y-1}$

So the inverse function is $\frac{x}{2x-1}$