Level sets are actually determined by a point in the codomain (or range) of your function. So if we have a function f : R3 R5, then a level set corresponds to a choice of point (a1, ..., a5 ) R5. Let f : R4 R2 be given by f (x, y, z, w) = (x^2 + y, x^2 + y^2 + z^2 + w^2 + y) find the level set of f at the point (0, 1).