Consider the function f(x) = sqrt(x^2 - 4) / (x^2 - 9). What is the domain of f?
Show the answer and explanation
Correct answer
A. (-∞, -3) ∪ (-3, -2] ∪ [2, 3) ∪ (3, ∞)
Principle or equation
The domain of a function is the set of all real numbers for which the expression is defined. For a square root, the radicand must be nonnegative. For a rational function, the denominator must not be zero.
Why this answer is correct
The radicand x^2 - 4 ≥ 0 gives x ≤ -2 or x ≥ 2. The denominator x^2 - 9 ≠ 0 gives x ≠ ±3. Combining, we get (-∞, -3) ∪ (-3, -2] ∪ [2, 3) ∪ (3, ∞).
Example
For f(x) = sqrt(x-1)/(x-2), domain is [1,2) ∪ (2,∞).
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