Hello, Link88!
Find and graph the domain of: .$\displaystyle f(x,y) \;=\; \sqrt{\frac{yx^2}{x^2+(y1)^2}}$
The radicand must be positive.
The denominator is always positive except at (0,1) where the function is undefined.
The numerator must be nonnegative: .$\displaystyle y  x^2 \:\geq \:0 \quad\Rightarrow\quad y \:\geq \:x^2$
. . This is the set of points on and above the parabola: $\displaystyle y \,=\,x^2$
The region looks like this: Code:
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      *      

where there is a "hole" at (0,1).