Topic: Graphing a non-principal branch

I'm wanting to graph the inverse function of x/ln(x), which is e^-W(-1/x), but it appears to be incomplete, I guess because it's multivalued. The parametric x(t)=t/ln(t), y(t)=t starting at e does the job, but is there a way to continue the graph of the W() function into a non-principal branch without resorting to the parametric expression? I tried x(t)=t, y(t)=e^-W(-1/t) but, of course, got the same result as a standard function.

Re: Graphing a non-principal branch

No, you cannot do it with W() because all functions returns a most one value. You already discovered how to do it with a parametric function. Another way is plotting the relation x=y/ln(y).