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一、有些数学题在形式结构上分别有其各自不同的特征,通过抓住这些特别显著的特征、标志,使得问题形象直观化,联想有关概念、定理、公式或方法,分析出内在联系,能使我们较灵活地找到转化变换的途径设对于任意实数x∈[-2,2],函数f(x)=lg(3a-ax-x2)总有意义,求实数a的取值范围。解法一:f(x)有意义,有3a-ax-x2>0,即x2+ax-3a<0在x∈[-2,2]时总成立,设g(x)=x2+ax-3a,即当x∈[-2,2]时,g(x)<0总成立。依抛物线y=g(x)的特征,将其定位,
First, some math problems have their own different characteristics in form and structure respectively. By grasping these distinctive features and signs, visualizing the problem image, associating with relevant concepts, theorems, formulas, or methods, we can analyze the internal relations, Let us be more flexible to find ways to transform the transformation for any real x ∈ [-2,2], the function f (x) = lg (3a-ax-x2) always makes sense, find the real a range of values. Solution 1: f (x) makes sense, with 3a-ax-x2> 0, that is, x2 + ax-3a <0 holds true for x∈ [-2,2] 3a, that is, when x∈ [-2,2], g (x) <0 holds. According to the characteristics of the parabola y = g (x), it is positioned,