Final answer:
The range of the composition of the functions (w°r)(x), assuming r(x) = 2 - x² and w(x) = x - 2, is [-∞, 0].
Step-by-step explanation:
The question is asking for the range of the composition of two functions (w°n)(x). However, it seems there's a typo, as 'n' is not defined. If we assume 'n' is meant to be 'r', we are looking for the range of (w°r)(x), which means applying w after r. From the given functions r(x) = 2 - x² and w(x) = x - 2, we first apply r to x, getting r(x), and then apply w to r(x). The result is w(r(x)) = w(2 - x²) = (2 - x²) - 2 = -x². Since the range of -x² is always less than or equal to 0, the range of (w°r)(x) is [-∞, 0].