Maybe "incorrect" is too strong a term but I think I see why it looks wrong (rather than "is wrong"). When curves go off to infinity (I know, that's pretty loose talk) and only a finite number of points approximate a curve where there is a discontinuity, the plotted extreme points get joined (inappropriately). If you are mainly interested in x >= 0, then the plot of x / Log[x] vs. x should look like

Same issue for the inverse.

I realize, what you was talking about in previous reply)

My first post contains 3 links. Two of them links on inverse function for x/ln(x). Wolfram alpha says that result of inversion is -xW(-1/x). There are also displayed two graphics mirrored relatively to dash-line y=x. So, those two graphics must be x/ln(x) and InverseFunction(x/ln(x)).

My question was "Why InverseFunction(x/ln(x)) = -xW(-1/x) and plot(-xW(-1/x)) looks different?" I didn`t know how actually -xW(-1/x) looks. Now, thanks for you, I understand that -xW(-1/x) is correct. Then InverseFunction(x/ln(x)) in wolfram alpha is incorrect, or I am doing something wrong?

Do you wanna to say, that InverseFunction in wolfram displays the real part and the imaginary part of the inverse? Then, why on Legend displays two caption x/log(x) and -xW(-1/x) (not re(...) and im(...)), or why, for example, InverseFunction(x^2) displays x^2 and sqrt(x) (not re[sqrt(x)] and im[sqrt(x)]).

I don't see anything in common between your and my pictures. And more, x/log(x) different from my picture. I got totally confused.

Thanks. ParametricPlot not exactly what I asked, but it has helped me in calculations. It`s just interesting, why the result of InverseFunction(x/ln(x)) = -xW(-1/x) and direct plot(-xW(-1/x)) looks different.

PS: One of links was incorrect. Have fixed it.