For all real x, the minimum value of 1 - x + x21 + x + x2 is:

Let f(x) be a function defined on [-1/2, 1/2] by f(x) = x - [x] - 1/2 for x ≠ 1/2 and f(1/2) = 0, where [x] represents the greatest integer function. Then:

The minimum value of 3{(x2 - 2)2 + 8} is:

Let u + v + w = 3, where u, v, w ∈ ℜ, and f(x) = u x2 + v x + w be such that f(x + y) = f(x) + f(y) + x y for all x, y ∈ ℜ. Then f(1) is equal to: