What is the domain of the function f(x) = sqrt(5 - x) / (x^2 - 3x - 4)?
Show the answer and explanation
Correct answer
A. (-∞, -1) ∪ (-1, 4) ∪ (4, 5]
Principle or equation
The domain consists of all real x such that the radicand is nonnegative and the denominator is nonzero.
Why this answer is correct
Radicand: 5 - x ≥ 0 => x ≤ 5. Denominator: x^2 - 3x - 4 = (x-4)(x+1) ≠ 0 => x ≠ 4 and x ≠ -1. Combine: x ≤ 5, x ≠ -1, x ≠ 4. In interval notation: (-∞, -1) ∪ (-1, 4) ∪ (4, 5].
Example
For f(x) = sqrt(x-2)/(x-3), domain is [2,3) ∪ (3,∞).
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