How would you write R(u, v)=(u^2, uv, v) ...

How would you write R(u, v)=(u^2, uv, v) in the form z=S(x, y)?

In[92]:=

  ParametricPlot3D[{u^2,u v,v},{u,0,2},{v,0,2}];

In[93]:=

  Show[%, ViewPoint->{0,1,0}];

I hope you can see that this is equivalent to z=y/Sqrt[x].

In[94]:=

  Plot3D[y/Sqrt[x],{x,.1,4},{y,0,4}];

In[95]:=

  Show[%, ViewPoint->{0,1,0}];