If domain of the function log e 6 x 2 + 5 x + 1 2 x - 1 + cos - 1 2 x 2 - 3 x + 4 3 x - 5 is α , β ∪ γ , δ , then 18 α 2 + β 2 + γ 2 + δ 2 is equal to

Step-by-step solution

We need to find the domain of the function log e 6 x 2 + 5 x + 1 2 x - 1 + cos - 1 2 x 2 - 3 x + 4 3 x - 5 . ⇒ 6 x 2 + 5 x + 1 2 x - 1 > 0   . . . . . ( 1 ) and ⇒   - 1 ≤ 2 x 2 - 3 x + 4 3 x - 5 ≤ 1 . . . . . . ( 2 ) Now From 1 , ⇒ 6 x 2 + 5 x + 1 2 x - 1 > 0 ⇒ ( 3 x + 1 ) ( 2 x + 1 ) ( 2 x - 1 ) > 0 Now we get the common region here as ⇒ x ∈ - 1 2 , - 1 3 ∪ 1 2 , ∞ . . . . . . . ( a ) From 2 we get that ⇒ - 1 ≤ 2 x 2 - 3