Final answer:
The domain of the function t(x)=(x+5)/(x²-2x-24) is (-∞, -4) ∪ (-4, 6) ∪ (6, ∞) in interval notation.
Step-by-step explanation:
The domain of a function is the set of all possible input values, or x-values, for which the function is defined. In this case, the function t(x)=(x+5)/(x²-2x-24) is defined for all values of x except the ones that would make the denominator equal to zero.
To find the domain, we need to solve the equation x²-2x-24=0. This equation can be factored to (x-6)(x+4)=0, which means that x=6 or x=-4.
Therefore, the domain of the function is (-∞, -4) ∪ (-4, 6) ∪ (6, ∞) in interval notation.