Final answer:
The domain of k(x) = 4/(81 - x^2) is (-∞, -9) U (-9, 9) U (9, ∞) in interval notation.
Step-by-step explanation:
The domain of k(x) = 4/(81 - x2) in interval notation can be found by considering the values of x that make the denominator nonzero, since dividing by zero is undefined. To find these values, set the denominator equal to zero and solve for x. The denominator 81 - x2 equals zero when x is equal to 9 or -9. Hence, the domain of k(x) is (-∞, -9) U (-9, 9) U (9, ∞) in interval notation.
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