Consider the function f(x) = sqrt(7 - x) / (x^2 - 2x - 8). What is the domain of f?
Show the answer and explanation
Correct answer
A. (-∞, -2) ∪ (-2, 4) ∪ (4, 7]
Principle or equation
The domain consists of all x such that the radicand is nonnegative and the denominator is not zero.
Why this answer is correct
Radicand: 7 - x ≥ 0 ⇒ x ≤ 7. Denominator: x^2 - 2x - 8 = (x-4)(x+2) ≠ 0 ⇒ x ≠ 4, -2. Thus domain is (-∞, -2) ∪ (-2, 4) ∪ (4, 7].
Example
For f(x) = sqrt(x)/(x-1), domain is [0,1) ∪ (1,∞).
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