The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value).
The domain of the function f(x) = 2x^2 + 5x - 12 / x + 4 is the set of all real numbers except x = -4, since division by zero is undefined. So the domain of the function is:
(-∞, -4) ∪ (-4, ∞)
The range of a function is the set of all possible output values (y-values) that the function can produce for values within the domain. The range of the function f(x) cannot be determined from its equation alone, as it depends on the behavior of the function over its entire domain. To determine the range, you would need to find the y-values for specific x-values within the domain and examine the overall behavior of the function.