What is the range of f(x) = (x² − 1)/(x² + 1)?

Correct answer: [−1, 1)

To determine the range, set t = x², so t ≥ 0. Then f = (t − 1)/(t + 1). Since t + 1 is positive, f + 1 = 2t/(t + 1) ≥ 0, which gives f ≥ −1. The value −1 is attained when t = 0, that is, x = 0. Also, f = 1 would require t − 1 = t + 1, an impossibility because it would give −1 = 1. More directly, 1 − f = 2/(t + 1) > 0, so f < 1 for every real x. As t increases from 0 without bound, f increases from −1 toward 1, reaching every intermediate value but never reaching 1. Therefore the range is [−1, 1), so option A is correct. The other choices either omit −1 or include the unattainable endpoint 1.