Question

Domain of the function \[ f(x) = \sqrt{\sin^{-1}(2x) + \frac{\pi}{6}} \text{ for real values of } x \]

• A. \([- \frac{1}{4}, \frac{1}{2}]\)
• B. \([- \frac{1}{2}, \frac{1}{2}]\)
• C. \([- \frac{1}{4}, \frac{1}{4}]\)
• D. \([- \frac{1}{2}, \frac{1}{9}]\)

Hint:

For functions involving inverse trigonometric functions, always ensure the argument of the inverse function is within its valid domain and that the expression inside the square root is non-negative for real-valued outputs.

Answer 1

The Correct Option is A