Question

Which inequality represents all values of x for which the product below is defined

Answer 1

Answer:

(-∞, -2) ∪ (0, ∞)

Step-by-step 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, ∞).