What is the domain of the function f(x) = sqrt(2x - 6) / (x - 5)?
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Correct answer
A. [3, 5) ∪ (5, ∞)
Principle or equation
For a square root, the radicand must be nonnegative. For a fraction, the denominator cannot be zero. Combine these conditions.
Why this answer is correct
The radicand 2x - 6 ≥ 0 gives x ≥ 3. The denominator x - 5 ≠ 0 gives x ≠ 5. Thus the domain is [3, 5) ∪ (5, ∞).
Example
For f(x) = sqrt(x - 1)/(x - 2), the domain is [1, 2) ∪ (2, ∞).
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