The function f(x,y,z) = 1/(x^2+y^2+z^2) has a domain defined as R^3 excluding the origin, specifically represented as \mathbb{R}^3 \setminus{\{0,0,0\}} or alternatively as the set {(x,y,z) | x^2 + y^2 + z^2 ≠ 0}. This indicates that the function is undefined at the point (0,0,0) where the denominator equals zero. The discussion confirms the correct representation of the domain for this multivariable function.
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