Answer:
(-∞, -2) ∪ (0, ∞)
Explanation:
Multiply together the (7x) and the (x+2), obtaining 7x^2 + 14x. This is the correct argument (input) to Answer A.
Since the domain of the square root function includes "all real numbers equal to or greater than 0," we set 7x^2 + 14x = to 0. This factors to the original 7x*(x+2), set equal to 0. The roots are 0 and -2.
These two values create three intervals: (-∞, -2), (-2, 0) and (0, ∞).
Choosing test numbers, one from each interval: {-5, -1, 1}.
7x^2 + 14x is + at x = -5, - at x = -1, and + at x = 1.
Thus, the domain of this function is (-∞, -2) ∪ (0, ∞). In other words, the product shown is defined on (-∞, -2) ∪ (0, ∞).