The domain of the function f x = sin - 1 2 x 2 - 3 + log 2 log 1 2 x 2 - 5 x + 5 , where t is the greatest integer function, is

Step-by-step solution

Given f x = sin - 1 2 x 2 - 3 + log 2 log 1 2 x 2 - 5 x + 5 For f x to be defined - 1 ≤ 2 x 2 - 3 < 1 ⇒ - 1 ≤ 2 x 2 - 3 < 2 ⇒ 2 < 2 x 2 < 5 ⇒ 1 < x 2 < 5 2 i.e. x ∈ - 5 2 , - 1 ∪ 1 , 5 2       . . . i and x 2 - 5 x + 5 > 0 ⇒ x - 5 - 5 2 x - 5 + 5 2 > 0 i.e. - ∞ , 5 - 5 2 ∪ 5 + 5 2 , ∞       . . . i i Also log 1 2 x 2 - 5 x + 5 > 0 ⇒ x 2 - 5 x + 5 < 1 ⇒ x 2 - 5 x + 4 &#6