The domain of the function f x = 2 sin - 1 ⁡ log 2 ⁡ 1 2 x 2 is

Step-by-step solution

For f x to be defined, we must have - 1 ≤ l o g 2 1 2 x 2 ≤ 1 ⇒ 2 - 1 ≤ 1 2 x 2 ≤ 2 1 as   t h e  b a s e = 2 > 1 ⇒ 1 ≤ x 2 ≤ 4 … . i Now, 1 ≤ x 2 ⇒ x 2 - 1 ≥ 0 i.e. x - 1 x + 1 ≥ 0 ⇒ x ≤ - 1 or x ≥ 1 … . i i Also, x 2 ≤ 4 ⇒ x 2 - 4 ≤ 0 i.e. x - 2 x + 2 ≤ 0 ⇒ - 2 ≤ x ≤ 2 … . . i i i From Equation i i and i i i , we get, the domain of f = - ∞ , - 1