What is the domain of the function f(x) = sqrt(3 - x) / (x^2 - 4)?
Show the answer and explanation
Correct answer
B. (-∞, -2) ∪ (-2, 2) ∪ (2, 3]
Principle or equation
The domain of a function with a square root requires the radicand non-negative, and the denominator cannot be zero.
Why this answer is correct
For sqrt(3 - x) to be defined, 3 - x ≥ 0 => x ≤ 3. The denominator x^2 - 4 ≠ 0 => x ≠ ±2. Combining gives x ≤ 3 and x ≠ -2, 2. In interval notation: (-∞, -2) ∪ (-2, 2) ∪ (2, 3].
Example
For f(x) = sqrt(x) / (x - 1), domain is [0, 1) ∪ (1, ∞).
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