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I have a function thats domain is defined for x and y values and for x^2+y^2>=1. I can only manage to plot it with the Plot3D command, but I want a regular 2D graph. I've tried defining it multiple different ways to get it to plot in 2D, but to no avail. Here is what I have done:

f[x_, y_] := 
x + (x/((x^2) + (y^2))) /; -2 <= x <= 2 && 0 <= y <= 2 && 
x^2 + y^2 >= 1;

When I try to plot this with the regular Plot[] command I get errors. Here is how I have graphed it in 3D, but 3D is not beneficial to me, I need it in 2D.

Plot3D[f[x, y] && x^2 + y^2 >= 1, {x, -2, 2}, {y, 0, 2}, 
PlotPoints -> 100, Mesh -> None];

OR

Plot3D[ConditionalExpression[x + x/(x^2 + y^2), x^2 + y >= 1], {x, -2,
2}, {y, 0, 2}]
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Are you looking for something like a DensityPlot or ContourPlot?

I've redefined your f[x_, y_] as it wasn't necessary to include all the extra conditions if you're only going to plot in a certain region anyways.

f[x_, y_] := x + x/(x^2 + y^2) /; x^2 + y^2 >= 1
DensityPlot[f[x, y], {x, -2, 2}, {y, 0, 2}, PlotLegends -> Automatic]
ContourPlot[f[x, y], {x, -2, 2}, {y, 0, 2}, PlotLegends -> Automatic]

Density plot of poster's function.

Contour plot of poster's function.

In these plots, colour represents the value of f[x, y] along the axes x and y. Of course you can use any colour scheme you desire, or even make it all a single colour if you like.

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