Answer
See explanation
Work Step by Step
The level surfaces for the function \(f(x,y,z)\) result \[ f(x,y,z) = k, \quad k \in \mathbb{R} \] Since \[ f(x,y,z) = (x-2)^2 + y^2 + z^2 \] results in the level surface: \[ (x-2)^2 + y^2 + z^2 = k \] We can note that \[ (x-2)^2 + y^2 + z^2 \geq 0 \] for any real \(x\), \(y\), \(z\), then \(k \geq 0\). Since \(k \geq 0\), \[ (x-2)^2 + y^2 + z^2 = k \] represents spheres centered at \((2,0,0)\) (denoted as \(C(2,0,0)\)) with radius \(r = \sqrt{k}\).
