论文部分内容阅读
1989年高考试卷上出现了这样一道题(理科第11题,文科第12题):已知f(x)=8+2x-x~2。如果g(x)=f(2-x~2),那么g(x)(A)在区间(-1,0)上是减函数。(B)在区间(0,1)上是减函数。(C)在区间(-2,0)上是增函数。(D)在区间(0,2)上是增函数。此系判定复合函数在局部区间上的单调性习题,由于此类习题尚不多见,已引起人们的兴趣。蔡水明先生已在本刊今年第3期《浅谈复合函数的教学》中第五部分讨论了这类问题,但总还觉得余意未尽,特此赘述如下。
Such a question appeared on the 1989 exam paper (science question 11 and liberal arts question 12): It is known that f(x)=8+2x-x~2. If g(x) = f(2-x~2) then g(x)(A) is a decreasing function in the interval (-1,0). (B) is a decreasing function in the interval (0,1). (C) is an increasing function over the interval (-2,0). (D) is an increasing function on the interval (0,2). This department determines the monotonic exercise of the compound function on the local interval. Since this kind of exercise is still rare, it has aroused people’s interest. Mr. Cai Shuiming has discussed this kind of issue in the fifth part of this issue of the journal “Teaching Compound Functions” in this year’s issue. However, he still feels that there is not enough content to be exhausted.