What is the domain of the real-valued function f(x) = sqrt(9 - x^2) / ln(x - 1)?
Answer and explanation
Correct answer: B. (1, 2) U (2, 3]
- Step 1: For sqrt(9 - x^2) >= 0: 9 - x^2 >= 0 => -3 <= x <= 3. Step 2. For ln(x - 1) to be defined: x - 1 > 0 => x > 1. Step 3. For denominator != 0: ln(x - 1) != 0 => x - 1 != 1 => x != 2. Step 4. Combining conditions: x in (1, 3] with x != 2 => (1, 2) U (2, 3]. Answer: (1, 2) U (2, 3]. Why not the others: (1, 3] fails to exclude x = 2 where denominator vanishes.
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