Final answer:
The domain of the function H(x) is all real numbers except 5 and -6, typically expressed in interval notation as: (-∞, -6) ∪ (-6, 5) ∪ (5, ∞). This is because division by zero is undefined, and at x=5 and x=-6 the denominator of the function becomes zero.
Step-by-step explanation:
The domain of a rational function consists of all real numbers except for those that would make the denominator of the function equal to zero, as division by zero is undefined. In the given function H(x)=(-8x²)/((x-5)(x+6)), the denominator becomes zero and thus undefined when x equals 5 and -6. Therefore, the domain of the function H(x) is all real numbers except 5 and -6.
To find these boundary values, you'd set the denominator equal to zero and solve:
(x-5)(x+6) = 0
Once you solve this equation, you find x = 5, and x = -6.
So the main answer is that the domain of the function H(x) are all real numbers except 5 and -6. This is usually written in interval notation as: (-∞, -6) ∪ (-6, 5) ∪ (5, ∞).
Learn more about Domain of a Function