Question

Let f(x) be a function such that f '(x) = log_1/3(log₃(sinx + a)). If f(x) is decreasing for all real values of x then

• A. a ∈ (1, 4)
• B. a ∈ (4, ∞)
• C. a ∈ (2, 3)
• D. a ∈ (2, ∞)

Answer 1

Answer: (B)

a ∈ (4, ∞)

Answer 2

We must have, log_1/3 (log₃(sinx + a)) < 0 ∀ x ∈ R

⇒ log₃(sinx + a) > 1 ∀ x ∈ R

⇒ sinx + a > 3 ∀ x ∈ R

⇒ a > 3 − sinx ∀ x ∈ R

⇒ a > 4