Final answer:
The domain of the function f(x) = -24/(x^2) + 8 is the set of all real numbers, since no real value of x will result in a zero denominator.
Step-by-step explanation:
The domain of a function is the set of all possible inputs (x-values) for which the function is defined.
In the function f(x) = -24/(x^2) + 8, we need to identify any values for x that might make the function undefined, which usually occurs where there may be a division by zero or taking the square root of a negative number.
For the given function, the only restriction comes from the denominator of the fraction x^2.
Since squaring any real number cannot produce a negative result, the only value to be excluded from the domain is the one that makes the denominator zero, which does not happen for any real number in this case.
Therefore, the domain of the function f(x) = -24/(x^2) + 8 is the set of all real numbers, since no real number will make the denominator zero.