Consider the function f(x) = sqrt(2x - 5) / (x^2 - 9). Which of the following is the domain of f?
Show the answer and explanation
Correct answer
A. [5/2, 3) ∪ (3, ∞)
Principle or equation
The domain of a function involving a square root and a rational expression requires the radicand to be nonnegative and the denominator to be nonzero.
Why this answer is correct
For sqrt(2x - 5), we need 2x - 5 ≥ 0, so x ≥ 5/2. For the denominator x^2 - 9 ≠ 0, so x ≠ ±3. Since 3 ≥ 5/2, we exclude x = 3 from the interval [5/2, ∞). The value -3 is not in [5/2, ∞) anyway. Thus the domain is [5/2, 3) ∪ (3, ∞).
Example
For f(x) = sqrt(x - 1)/(x - 2), the domain is [1, 2) ∪ (2, ∞).
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