Final answer:
The formula for the function f(x, y, z) whose level surface is a sphere of radius 2 centered at the origin is f(x, y, z) = x^2 + y^2 + z^2.
Step-by-step explanation:
To find a formula for a function f(x, y, z) whose level surface is a sphere of radius 2 centered at the origin, we need to consider the equation of a sphere. The equation of a sphere centered at the origin is given by x^2 + y^2 + z^2 = r^2, where r is the radius. Since the radius of the given sphere is 2, the equation of the sphere is x^2 + y^2 + z^2 = 4.
This equation represents the level surface f = 4, where f(x, y, z) is the function we are looking for. So, the formula for the function f(x, y, z) is f(x, y, z) = x^2 + y^2 + z^2.