一、问题的提出近期出版的“三点一测”数学丛书,数学题典等书,在讲到复合函数单调性时,其中都有这样一段文字:“一般地,y=f[g(x)]中,如果t=g(x)在区间[a,b]上是单调增(减)函数且y=f(t)在区间(g(a),g(b))[(或在(g(b),g(a))]上是单调函数,那么y=[g(x)]在[a,b]上具有单调性。”且有如下结论: First, the issue of the recent publication of “three points a test” mathematics series, mathematical problem code book, etc., when talking about the monotony of the composite function, which has such a paragraph: "Generally, y = f [g (x In ]], if t=g(x) is a monotonically increasing (decreasing) function in the interval [a,b] and y=f(t) is in the interval (g(a), g(b))[(or (g(b),g(a))] is a monotonous function, then y=[g(x)] has monotonicity on [a,b].” And there are the following conclusions: