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Determine the domain of the following rational function: f(x) = \frac{(x+8)(x-2)}{(x-5)(x+6)(x-3)} A. (-∞,...

9. Determine the domain of the following rational function:
f(x) = \frac{(x+8)(x-2)}{(x-5)(x+6)(x-3)}
A. (-∞, -6) ∪ (-6, 5) ∪ (5, ∞)
B. (-∞, -6) ∪ (-6, 3) ∪ (3, 5) ∪ (5, ∞)
C. (-∞, -2) ∪ (-2, 5) ∪ (5, ∞)
D. (-∞, -3) ∪ (-3, 5) ∪ (5, ∞)

Answer

Answer: The domain of the function is all real numbers except where the denominator is zero. The denominator is zero at x = 5, x = -6, and x = 3. Therefore, the domain is:

  1. B. (-∞, -6) ∪ (-6, 3) ∪ (3, 5) ∪ (5, ∞)

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