JEE Main202229 Jun 2022Morning ShiftMathematicsFunctionsActual
The domain of the function cos - 1 2 sin - 1 1 4 x 2 - 1 π is
Options
- A- ∞ , - 1 2 ∪ 1 2 , ∞ ∪ 0
- B- ∞ , - 1 2 ∪ 1 2 , ∞
- C- ∞ , - 1 2 ∪ 1 2 , ∞ ∪ 0
- DR - - 1 2 , 1 2
Correct answer
A. - ∞ , - 1 2 ∪ 1 2 , ∞ ∪ 0
Step-by-step solution
f x = cos - 1 2 sin - 1 1 4 x 2 - 1 π Case I: - 1 ≤ 1 4 x 2 - 1 ≤ 1 ⇒ 4 x 2 - 1 ≥ 1 or 4 x 2 - 1 ≤ - 1 and 4 x 2 - 1 ≠ 0 ∴ x 2 ≥ 1 2 or x 2 ≤ 0 ⇒ x = 0 and x ≠ ± 1 2 ∴ x ∈ - ∞ , - 1 2 ∪ 1 2 , ∞ ∪ 0 Case II: - 1 ≤ 2 sin - 1 1 4 x 2 - 1 π ≤ 1 ⇒ - π 2 ≤ sin - 1 1 4 x 2 - 1 ≤ π 2 which is always true. Hence, x ∈ - ∞ , - 1 2 ∪ 1 2 , ∞ ∪