The function f(x) = x - sin x is:

The function f(x) = x - sin x is:

• A. Strictly increasing for all real x
• B. Strictly decreasing for all real x
• C. Increasing only in (0, π)
• D. Decreasing only in (0, π)

Answer: A) Strictly increasing for all real x

Explanation: f'(x) = 1 - cos x. Since cos x ≤ 1 for all x, 1 - cos x ≥ 0. The derivative is zero only at discrete points (x = 2nπ), making it strictly increasing on R.