If the domain of the function f x = cos - 1 2 - | x | 4 + log e ( 3 - x ) - 1 is [ - α , β ) - γ , then α + β + γ is equal to :

Step-by-step solution

Given: y = cos - 1 2 - x 4 + log 3 - x - 1 ⇒ - 1 ≤ 2 - x 4 ≤ 1 ⇒ - 4 ≤ 2 - x ≤ 4 ⇒ - 6 ≤ - x ≤ 2 ⇒ - 2 ≤ x ≤ 6 ⇒ x ≤ 6 ⇒ - 6 ≤ x ≤ 6 . . . i Also, 3 - x > 0 and 3 - x ≠ 1 ⇒ x ≠ 2 . . . i i and x < 3 . . . i i i Using i , i i and i i i we get, ⇒ x ∈ [ - 6 , 3 ) - 2 So, on comparing with x ∈ [ - α , β ) - γ we get, ⇒ α + β + γ = 6 + 3 + 2 = 11