函数定义域值域求法.ppt
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求函数值 1:已知 2:若 3:函数满足 求函数值 4: 5:已知 五、利用反比例函数法 * Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 几类函数的定义域: (1)如果f(x)是整式,那么函数的定义域是实数集R . (2)如果f(x)是分式,那么函数的定义域是使分母不等于零 的实数的集合 . (3)如果f(x)是二次根式,那么函数的定义域是使根号内的式子大于或等于零的实数的集合. (5)如果f(x)是由几个部分的数学式子构成的,那么函数定义域是使各部分式子都有意义的实数集合.(即求各集合的交集) (6)满足实际问题有意义 (4)如果求 ,那么函数的定义域是使 f(x)不等于0的实数的集合. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 函数的定义域问题(一) 例:求下列函数的定义域: 分析:解题的关键就是明确使各函数表达式有意义的条件。 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 二、求抽象函数的定义域 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 设函数y=f(x)的定义域为[0,1],求下列函数的定 义域.(1) (2)y=f(x+a)+f(x-a). 题型二 抽象函数的定义域 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 【分析】正确理解函数定义域的概念,理解函数f(x)定义域 是x的取值范围. (1)已知函数f(x)的定义域是[0,4],求函数f(x2)的定义域; (2)已知函数f(2x+1)的定义域是[-1,3],求函数f(x)的定义域; (3)已知函数f(x2-2)的定义域是[1,+∞),求函数 的定义域. 返回 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. ① 故由① ②可知 ② Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 练习 【分析】利用函数定义域为R,mx2-6mx+m+8≥0在R上恒成立建立不等式或不等式组求m. 【评析】二次函数定义域为R,二次不等式在R上恒成立,也可转化为二次函数与二次方程关系求解. 函数y=
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