OSSD反函数的概念

　大家好，今天我们来聊一下OSSD反函数的概念。

　　Inverse functions are a special class of functions that undo each other. The input and output values for two inverse functions, f(x) = 2x + 1   and g(x) = x-12 ,  are shown below:

　　反函数是一类相互撤销的特殊函数。两个反函数的输入和输出值如下所示：

Notice that the output of the first function, f(x), becomes the input for the second function, g(x). The function g(x) undoes what f(x) does. The ordered pairs of g(x) can be found by switching the coordinates in each ordered pair of f(x).

　　Recall that a relation is a set of ordered pairs. The inverse of a relation can be found by interchanging the domain and the range of the relation:

　　请注意，第一个函数f（x）的输出成为第二个函数g（x）的输入。

　　回想一下，关系是一组有序对。反函数关系可通过互换关系的域和范围来找到。

　　You will also recall that a function is a special relation. For each element in the domain of a function, there is exactly one element in the range. If the inverse of a function f(x), is also a function, it is called the inverse function of f(x). The inverse function is represented by f-1(x).

　　The notation of  f-1 is read as 'the inverse of f' or simply 'f inverse'. Please note that -1  is not an exponent（指数）, therefore, f-1≠ 1f

　　The table shows ordered pairs belonging to a function f(x). Determine  f-1(x), graph  f(x) and its inverse and state the domain and range of  f(x) and its inverse.

　　下表显示了属于函数f（x）的有序对。接下来我们确定 f-1(x)，图及其逆，并说明其逆的定义域和值域。

　　In this example, switch the x and y coordinates, and then plot the points.

　　在此示例中，切换x和y坐标，然后绘制点

　　Notice that switching the x and y coordinates reflects the graph of f(x)  in the line  y = x.

　　请注意，切换和坐标会转换直线中的x与y关系

Notice below that the domain of f(x) is the range of f-1(x) , and the range of f(x) is the domain of f-1(x) :

　　请注意，上图中f(x)的定义域是f-1(x) 的值域，f(x)的值域是f-1(x) 的定义域。这就是求f(x)反函数的方法。

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