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近年来复合函数中的零点问题已经成为各地高考(模拟)卷中考查热点。本文采撷几道典型试题并予以深度解析,旨在探索题型规律,揭示解题方法。一、考查零点定义例1已知函数f(x)=(m-n/3)·3~x+x~2+2nx,记函数y=f(x)的零点构成的集合为A,函数y=f[f(x)]的零点构成的集合为B,若A=B,则m+n的取值范围为____。解析设f(x_1)=0,则f(f(x_1))=f(0),
In recent years, the zero point in the composite function has become a test hotspot around the college entrance examination (simulation). This paper picks a few typical questions and depth analysis, the purpose is to explore the type of questions, reveal the problem-solving methods. First, check the definition of zero Example 1 known function f (x) = (mn / 3) · 3 ~ x + x ~ 2 +2 nx, remember function y = f (x) zero set consisting of A, y = The set of zero points of f [f (x)] is B, and if A = B, the range of m + n is ____. Analytical f (x_1) = 0, then f (f (x_1)) = f (0),