What is the domain of the function f(x) = sqrt(4 - x^2) / (x - 1)?
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Correct answer
A. [-2, 1) ∪ (1, 2]
Principle or equation
The domain consists of all real x for which the expression is defined: the radicand must be nonnegative and the denominator must not be zero.
Why this answer is correct
The square root requires 4 - x^2 ≥ 0, so -2 ≤ x ≤ 2. The denominator x - 1 ≠ 0, so x ≠ 1. Combining gives [-2, 1) ∪ (1, 2].
Example
For f(x) = sqrt(x - 1)/(x - 2), domain is [1, 2) ∪ (2, ∞).
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