Final answer:
The domain of the function is all points inside or on the circle x^2 + y^2 ≥ 36.
Step-by-step explanation:
The domain of a function is the set of all possible values of x for which the function is defined. In this case, we have the function f(x,y) = √(x^2 + y^2 - 36). Since the square root function is defined only for non-negative values, x^2 + y^2 - 36 must be greater than or equal to 0. Solving this inequality: x^2 + y^2 - 36 ≥ 0, we get x^2 + y^2 ≥ 36.
This is the equation of a circle centered at the origin with radius 6 units. Therefore, the domain of our function is the set of all points inside or on the circle. In set notation, the domain can be written as x^2 + y^2 ≥ 36.
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