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For which values of a does the equation sin⁻¹x = 2 sin⁻¹a admit a solution?

1. |a| ≤ 1/√2
2. 1/2 ≤ |a| ≤ 1/√2
3. a can be any real number
4. |a| < 1/2

Correct answer: |a| ≤ 1/√2

Solution

The equation sin⁻¹x = 2 sin⁻¹a requires that the values of sin⁻¹a must be within the range of the arcsine function, which is defined for inputs between -1 and 1. The maximum value of 2 sin⁻¹a occurs when |a| is at most 1/√2, ensuring that the output remains within the valid range of the arcsine function.

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