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