Consider the function f(x) = sqrt(8 - 2x) / (x^2 - 3x - 4). What is the domain of f?
Show the answer and explanation
Correct answer
B. (-∞, 4] except x = -1
Principle or equation
The domain consists of all real x such that the radicand is nonnegative and the denominator is not zero.
Why this answer is correct
Radicand: 8 - 2x ≥ 0 → x ≤ 4. Denominator: x^2 - 3x - 4 = (x - 4)(x + 1) ≠ 0 → x ≠ 4 and x ≠ -1. Since x ≤ 4 already excludes x = 4, the domain is (-∞, 4] except x = -1.
Example
For f(x) = sqrt(6 - 2x)/(x^2 - 5x + 6), domain is (-∞,3] except x=2.
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