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函数的单调性是函数的一个极其重要的性质,在高三的复习中经常会碰到有关函数单调性求解的问题,有的同学感到束手无策．如何去研究呢?下面通过例子来说明此类问题的求解思路．一、掌握几种常见函数的单调性,会求复合函数的单调区间复习过程中要熟练掌握几种常见函数(如一次函数、二次函数、反比例函数、指、对数函数及三角函数)的单调性,并能利用复合函数单调性的性质求解复合函数的单调区间．例1 (1989年高考)已知f(x)=8+2x- x2,如果g(x)=f(2-x2),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
The monotonicity of a function is an extremely important property of the function. In the third year of a review, it often encounters the problem of solving the monotonicity of the function, and some students feel helpless. How to study it? The following examples to illustrate the solution of such problems. First, grasp the monotony of several common functions, monotonous range of complex functions will be required to review several familiar functions (such as primary function, quadratic function, inverse proportion function, finger, logarithm function and trigonometry function) Monotonicity, and can take advantage of the monotonicity of the composite function to solve the monotonic interval of the composite function. Example 1 (1989 college entrance examination) Given that f (x) = 8 + 2x- x2 and g (x) = f (2-x2), then g ) Is the decreasing function (B) in the interval (0,1) is the decreasing function (C) is the increasing function in the interval (-2,0) (D) is the increasing function in the interval (0,2)