The set of all values of x for which the function f(x) = ||x| - 1| is differentiable is:

Consider the following three statements for the function f : (0, ∞) → ℜ defined by f(x) = |loge x| - |x - 1|: I. f is differentiable at all x > 0. II. f is increasing in (0, 1). III. f is decreasing in (1, ∞). Which of the statements given above is/are TRUE?

If f and g are two real-valued continuous functions such that f + g and f - g are differentiable, then which of the following statements is true?