What is the domain of the function f(x) = sqrt(x + 3) / (x^2 - 4)?
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Correct answer
A. [-3, 2) ∪ (2, ∞)
Principle or equation
The domain of a function is the set of all real numbers for which the function is defined. For a square root, the radicand must be nonnegative. For a rational expression, the denominator cannot be zero.
Why this answer is correct
The radicand x + 3 must be ≥ 0, so x ≥ -3. The denominator x^2 - 4 = (x - 2)(x + 2) cannot be zero, so x ≠ 2 and x ≠ -2. Since -2 is already excluded by x ≥ -3, the domain is [-3, 2) ∪ (2, ∞).
Example
For f(x) = sqrt(x - 1) / (x - 3), domain is [1, 3) ∪ (3, ∞).
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