What is the domain of the function f(x) = sqrt(x^2 - 9) / (x - 2)?
Show the answer and explanation
Correct answer
A. (-∞, -3] ∪ [3, ∞) excluding x = 2
Principle or equation
The radicand of a square root must be nonnegative, and the denominator cannot be zero.
Why this answer is correct
The radicand x^2 - 9 ≥ 0 gives x ≤ -3 or x ≥ 3. The denominator x - 2 ≠ 0 gives x ≠ 2. Since 2 is not in the intervals anyway, the domain is (-∞, -3] ∪ [3, ∞).
Example
For f(x) = sqrt(x - 1) / (x - 3), radicand gives x ≥ 1, denominator gives x ≠ 3, so domain [1, 3) ∪ (3, ∞).
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