What is the domain of the function f(x) = sqrt(9 - x^2) / (x^2 - 4)?
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Correct answer
A. [-3, 3] \ {-2, 2}
Principle or equation
The radicand must be nonnegative and the denominator must not be zero.
Why this answer is correct
For sqrt(9 - x^2) to be defined, 9 - x^2 ≥ 0, so -3 ≤ x ≤ 3. Denominator x^2 - 4 ≠ 0 gives x ≠ ±2. Thus domain is [-3, 3] \ {-2, 2}.
Example
For sqrt(4 - x^2)/(x - 1), domain is [-2, 2] \ {1}.
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