If the function f(x) = {kx + 1, if x ≤ π, cos x, if x > π} is continuous at x = π, then the value of k is:
Correct: B
For f(x) to be continuous at x = π, the left-hand limit (LHL) and the right-hand limit (RHL) must be equal to the value of the function at x = π. LHL = lim (x→π⁻) (kx + 1) = kπ + 1. RHL = lim (x→π⁺) cos x = cos π = -1. f(π) = kπ + 1. For continuity, LHL = RHL, so kπ + 1 = -1. This implies kπ = -2, so k = -2/π.