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函数的定义域、对应关系、函数的值域是函数概念的三要素,其中函数的值域可由函数的定义域和对应关系唯一确定.在解决某些数学问题时,若能恰当、巧妙地构出函数,借助其值域解题,常可获得独特、简捷的解法,曲经通幽,回味无穷!现举数例说明,供参考.例1已知函数f(x)=(4x~2-7)/(2-x),g(x)=x~3-3a~2x-2a(a≥1).若对于?x_1∈[0,1],总?x_0∈[0,1],使得g(x_0)=f(x_1)成立,求实数a的取值范围.
The domain of functions, the correspondence, and the range of functions are the three elements of the concept of functions. The range of functions can be uniquely determined by the domain and corresponding relationship of the functions. If certain mathematical problems are solved, they can be properly and skillfully constructed. A function, with the aid of its value range, can often obtain a unique, simple solution, Qu pass through, endless aftertaste! Now give a few examples, for reference. Example 1 Known function f (x) = (4x ~ 2 -7)/(2-x), g(x)=x~3-3a~2x-2a(a≥1). If ?x_1∈[0,1], the total x_0∈[0,1] , making g(x_0)=f(x_1) true, find the range of real numbers a.