（1）∵∀x∈R，都有ax＞0，∴ax+1＞1，故函数f（x）=ax−1ax+1（a＞0且a≠1）的定义域为实数集R．∵f（x）=ax−1ax+1=1-2ax+1，而ax＞0，∴ax+1＞1，∴0＜2ax+1＜2，∴-2＜-2ax+1＜0，∴-1＜1-2ax+1＜1．即-1＜f（x...