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I need some help getting RegionPlot to display. Running this code:

region[z_] := Re[z] >= 1;
f[z_] := 1/z;
g = InverseFunction[f];

h[z_] = 1+1/z;
hin = InverseFunction[h];
hp = RegionPlot[region[hin[g[x + I y]]], {x, 0, 1}, {y, -0.5, 0.5}]

h2[z_] = 2+1/z;
h2in = InverseFunction[h2];
h2p = RegionPlot[region[h2in[g[x + I y]]], {x, 0, 1}, {y, -0.5, 0.5}]

h3[z_] = 3+1/z;
h3in = InverseFunction[h3];
h3p = RegionPlot[region[h3in[g[x + I y]]], {x, 0, 1}, {y, -0.5, 0.5}]

displays three disks decreasing in size, in the complex plane. However, when I try to run the fourth:

h4[z_] = 4+1/z;
h4in = InverseFunction[h4];
h4p = RegionPlot[region[h4in[g[x + I y]]], {x, 0, 1}, {y, -0.5, 0.5}]

The resulting plot is empty. I think because the circle is so small, Mathematica ignores it. Is there a way to increase the resolution or something like that, to get Mathematica to display small images?

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You could set more initial points:

RegionPlot[region[h4in[g[x + I y]]], {x, 0, 1}, {y, -0.5, 0.5}, 
 PlotPoints -> 30]

enter image description here

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  • $\begingroup$ That is exactly what I needed, thank you! $\endgroup$ – Daniel Feb 14 at 8:57

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