If the domain of the function f x = log e 4 x 2 + 11 x + 6 + sin - 1 4 x + 3 + cos - 1 10 x + 6 3 is ( α , β ] , then 36 α + β is equal to

Step-by-step solution

Given that f x = log 4 x 2 + 11 x + 6 + sin - 1 4 x + 3 + cos - 1 10 x + 6 3 We know that the domain of A x + B x + C x is D A ∩ D B ∩ D C . Let us find the domain of log 4 x 2 + 11 x + 6 . We know that domain of log f x is f x > 0 . ⇒ 4 x 2 + 11 x + 6 > 0 ⇒ 4 x 2 + 8 x + 3 x + 6 > 0 ⇒ 4 x + 3 x + 2 > 0 ⇒ x ∈ - ∞ , - 2 ∪ - 3 4 , ∞ Domain of log 4 x 2 + 11 x + 9 is x ∈ - ∞ , - 2 ∪ - 3 4 , ∞ . Let us find the domain of