Question

The domain of the function f(x)=sin⁻1(log₂((1)/(2)x²)) is

• A. [ -2,-1 ] ∪ [ 1,2 ]
• B. ( -2,-1 ] ∪ [ 1,2 )
• C. [ -2,-1 ) ∪ ( 1,2 ]
• D. ( -2,-1 ) ∪ ( 1,2 )

Hint:

For inverse trigonometric functions, always ensure the argument lies in [-1,1].

Answer 1

The Correct Option is A

Step 1: For sin⁻1(·), -1 ≤ log₂((1)/(2)x²) ≤ 1 Step 2: Convert to exponential form: 2⁻1 ≤ (1)/(2)x² ≤ 2¹ 1 ≤ x² ≤ 4 Step 3: Taking square roots: x ∈ [-2,-1] ∪ [1,2]