The expression is real if and only if -(x + 1)2 ≥ 0, that is, (x + 1)2 ≤ 0. The only way a squared number can be less than or equal to zero is for it to equal zero, so (x + 1)2 = 0, and (x + 1) = 0 or -(x + 1) = 0. In either case, x = -1. The answer is (b).
a real number?