已知函数f（x）=lg[（m2﹣3m+2）x2+2（m﹣1）x+5]，如果函数f（x）的值域为R，求实数m的取值范围．

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已知函数f（x）=lg[（m²﹣3m+2）x²+2（m﹣1）x+5]，如果函数f（x）的值域为R，求实数m的取值范围．

上一题下一题 0.0难度选择题更新时间:2016-01-11 05:26:56

解：令g（x）=（m²﹣3m+2）x²+2（m﹣1）x+5，

如果函数f（x）的值域为R，则x去任何值都要g（x）能取到任意的正数．即g（x）＞0．

当m²﹣3m+2=0时，即m=1或2．

经验证当m=1时，g（x）=5＞0恒成立，故m=1．

当m²﹣3m+2≠0时，根据二次函数性质，要使的函数值取得所有正在值，只需

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