Final answer:
The domain of the function f(x) = (x³ + 27) / (x+3) is (-∞, -3) U (-3, ∞).
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. To determine the domain of the function f(x) = (x³ + 27) / (x+3), we need to consider any restrictions on the x-values that would make the function undefined. In this case, the only restriction is that the denominator, (x+3), cannot be equal to zero. So, we set x+3 = 0 and solve for x. x = -3 is the only value that makes the function undefined. Therefore, the domain of the function is all real numbers except x = -3.
Using interval notation, we can represent the domain as (-∞, -3) U (-3, ∞). This means that the function is defined for all values less than -3 and all values greater than -3.