Yes. The link you provided (shown below) shows two curves and explicitly states that it is showing the real and the imaginary part of the inverse. So I was trying to determine why you were saying that one of the curves was wrong.

Was there another link that I didn't see that shows the issue you raise?

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.

Accidentally duplicated

Mathematica definitely gives the same values (where I've plotted the real part of the inverse using the two definitions):

f[x_] := x/Log[x];
fInverse = InverseFunction[f];
Plot[{Re[fInverse[x]], Re[-x ProductLog[-1/x]]}, {x, -15, 15}, 
 PlotStyle -> {{Thickness[0.05], LightBlue}, {Thin, Red}}, 
 PlotRange -> {{-15, 15}, {-1, 3}}]

with output

In Wolfram Alpha where is it that you see the wrong plot? The link you show displays the real part and the imaginary part of the inverse and not the original function and its inverse.

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.