For each of the following functions, find out whether the given expression can be solved for z in a nonempty, open set V containing (0, 0, 0). Is the solution differentiable near (0, 0)?
a) xyz + sin(x + y + z) = 0
b) x2 + y2 + z2 + √sin(x2 + y2) + 3z + 4) = 2
c) xyz(2 cos y - cos z) + (z cos x: - x cos y) = 0
d) x + y + z + g(x, y, z) = 0, where g is any continuously differentiable function which satisfies g(0,0,0) = 0 and gz(0,0,0) > 0