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Find the domain of f(x) = sin(sqrt(1 - x²)) + sqrt(x + 2) + 1/log₁₀((x + 1)/x).

1. (0, 1]
2. [-1, 1]
3. (0, 1)
4. [-1, 0) U (0, 1]

Correct answer: (0, 1]

Solution

Intersect the conditions: x in [-1,1] from the first root, x >= -2 from the second, and (x+1)/x > 0 (i.e. x < -1 or x > 0) from the logarithm. The log is never 0 since (x+1)/x = 1 has no solution.

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