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Determine the domain of the following rational function: f(x) = \frac{(x + 4)(x - 9)}{(x + 1)(x - 6)(x +...

1. Determine the domain of the following rational function:
f(x) = \frac{(x + 4)(x - 9)}{(x + 1)(x - 6)(x + 4)}
A. (-∞, -4) ∪ (-4, 0) ∪ (6, ∞)
B. (-∞, -1) ∪ (-1, 4) ∪ (4, 9) ∪ (9, ∞)
C. (-∞, -4) ∪ (-4, -1) ∪ (-1, 6) ∪ (6, ∞)
D. (-∞, -1) ∪ (-1, 6) ∪ (6, ∞)

Answer

Answer: D. (-∞, -1) ∪ (-1, 6) ∪ (6, ∞)

Explanation: The domain of the function is all real numbers except where the denominator is zero. The denominator is zero at x = -1, x = 6, and x = -4. However, x = -4 is also a zero of the numerator, which means it is a removable discontinuity. Therefore, the domain excludes x = -1 and x = 6.

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