What is the domain of the function f(x) = sqrt(4 - x^2) / (x - 3)?
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Correct answer
A. [-2, 2]
Principle or equation
The domain consists of all real numbers 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, which gives -2 ≤ x ≤ 2. The denominator x - 3 is zero at x = 3, but x = 3 is not in [-2,2], so the domain is simply [-2,2].
Example
For f(x) = sqrt(1 - x^2) / (x - 2), domain is [-1,1] because x=2 is not in the interval.
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