Given: f (x) = ax + 3 sin x + 4 cos x We have to find the interval for a such that f (x) is invertible Differentiating (i) w.r.t. x . we get f'(x) = a + 3 cos x - 4 sin x ... (ii) If f (x) is invertible, then f'(x) > 0 for all x or f'(x) < 0 for all x . ⇒ a + 3 cos x - 4 sin x > 0 for all x or a + 3 cos x - 4 sin x < 0 [Using (ii)] ⇒ a - 5 > 0 or a + 5 < 0 [Using Maximum and mrnimum values of trigonometric functions] ⇒ a > 5 or a < - 5 ⇒ a ∊ (- ∞, - 5) U (5 , ∞) Hence, option 'B' is correct