How to inverse $f(x)=x^\frac{1}{x-1}$

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I have tried a couple of approaches to inversing it, but I really don't know any strategies or methods. I don't even know if it's possible or how to figure out if it is possible, so I'm asking how to know if you can inverse or not as well. $f(x)=x^\frac{1}{x-1}$