What exactly does the anonymous JavaScript function f => f do?

f => f is similar* to function(f){ return f; }

So close, but not quite what you expected.

_{* - as has been pointed out in comments, there are subtle differences, but for the sake of your question, I don't think they are particularly relevant. They are very relevant in other situations.}

f => f is the identity function. It simply returns the argument that was passed in.

This function is often used as a default values for transformation processes, since it doesn't perform any transformation.

Is f => f equivalent to () => {} an empty anonymous function?

No. The empty function doesn't return anything. The identity function returns the passed in argument.