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Solve for real x: arcsin( sin( (2x² + 4)/(1 + x²))) < pi - 3.

1. x belongs to (-1, 1)
2. x belongs to (-2, 2)
3. x belongs to (0, 1)
4. x belongs to all real numbers

Correct answer: x belongs to (-1, 1)

Solution

Rewrite the argument as 2 + 2/(1 + x²), which lies in (2, 4]. On this range arcsin(sin t) = pi - t, turning the inequality into a simple condition on t.

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