Final answer:
The domain of the function f(x) = (x+10)/(x^2+5x-24) is (-∞, -8) ∪ (-8, 3) ∪ (3, ∞) in interval notation. Therefore,The domain of the function f(x) is (-∞, -8) ∪ (-8, 3) ∪ (3, ∞) in interval notation.
Step-by-step explanation:
The domain of a function is the set of all possible input values. For the given function f(x) = (x+10)/(x^2+5x-24), we need to find the values of x for which the function is defined.
The denominator of the function cannot be equal to zero, so we set it equal to zero and solve for x.
The domain of the function is the set of all real numbers except for the values that make the denominator zero.
x^2 + 5x - 24 = 0
(x+8)(x-3) = 0
x = -8 or x = 3
The domain of the function f(x) is (-∞, -8) ∪ (-8, 3) ∪ (3, ∞) in interval notation.
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