高一数学必须修读1复合函数定义域的求法.ppt

1.2.4 复合函数定义域的求法 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 复合函数的定义: 如果y是u的函数，记为y=f(u),u 又是x的函数，记为u=g(x),且g(x)的值域与f(u)的定义域的交集不空，则确定了一个y关于x的函y=f[g(x)],这时y叫x的复合函数，其中u叫中间变量，y=f(u)叫外层函数，u=g(x)叫内层函数. 即：x → u → y Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 复合函数的定义域的求法： 若复合函数y=f[g(x)]，外函数y=f(u)，内函数u=g(x)： (1)f(x)的定义域就是g(x)的值域.若f(x)的定义域为D，则y=f[g(x)]的定义域是使 有意义的x的集合. (2)y=f[g(x)]的定义域为D，则g(x)在D上的取值范围(g(x)的值域)即为f(x)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. 复合函数求定义域的几种题型： 解: 由题意知: 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. 解： 由题意知: Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 练习 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 题型四：　已知函数的定义域，求含参数的取值范围 (1)当K=0时, 3≠0成立 解: 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. 解:∵定义域是R, Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.