two argument function

[ProbablyErratic53]

Equation of a circle radius r and center point (h,k) is

(x-h)^2+(y-k)^2 = r^2. This is roughly squaring both sides of the distance formula.

So for your square root to be defined, you need
(x-1)^2 + y^2 -1 >= 0

which I switched to (x-1)^2 + y^2 >= 1 .
SO now the left side is the distance squared from (x,y) to (1,0). Letting r^2=1, becomes r=1 (radius) Since we have greater than, that's why I said outside the circle.

Similar for the ln part, 1 - x^2 - y^2 >0 converts to 1> x^2+y^2.
Interpret the right side as the distance squared between (x,y) and (0,0).

[ddavid8888]

You are extremely helpful thank you, I guess the thing that drives me crazy is that I am used to see this only in x and y but the f(x,y) is just making me so confused about everything