Question

f(x) be a differentiable function such that f '(x)=

$\frac { 1 } { \left( \log _ { 3 } \left( \log _ { 1 / 4 } ( \cos x + a ) \right) \right) }$ . If f(x) is increasing for all values of x then

• A. a ∈ (5, ∞)
• B. a ∈ (1, 5/4)
• C. a ∈ (5/4, 5)
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

For f(x) to be increasing ∀ x ∈ R, We must have log₃ (log_1/4 (cosx + a)) > 0 ∀ x ∈ R

⇒ 0 < cosx + a < $\frac { 1 } { 4 }$ ∀ x ∈ R

⇒ −cosx < a < $\frac { 1 } { 4 }$ − cosx ∀ x ∈ R

⇒ 1 < a < $\frac { - 3 } { 4 }$ , which is not possible