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一、求函数的反函数例1 求函数y=-(1-x2)~(1/2)(-1≤x≤0)的反函数. 解析由y=-(1-x2)~(1/2)知y2=1-x2(-1≤x≤0), 则x2=1-y2.由于-1≤x≤0,所以x= -(1-y2)~(1/2)(1≤y≤0),所以反函数为y=-(1-x2)~(1/2)(-1≤x≤0). 点评由反函数的定义求反函数一般应分以下步骤:(1)由已知解析式y=f(x)反求出x=Φ(y);(2)交换x=Φ(y)中x、y的位置;(3)求反函数的定义域(一般可通过求原函数的值域的方法求反函数的定义域).
First, find the inverse function of the function Example 1 Find the function y=-(1-x2) ~ (1/2) (-1 ≤ x ≤ 0) of the inverse function. Analysis by y =- (1-x2) ~ (1 /2) Know that y2=1-x2(-1≤x≤0), then x2=1-y2. Since -1≤x≤0, x= -(1-y2)~(1/2)(1) ≤y≤0), so the inverse function is y=-(1-x2)~(1/2)(-1≤x≤0). Comments The negation function defined by the inverse function should generally be divided into the following steps: (1 ) Reverses x=Φ(y) from the known analytical formula y=f(x); (2) Exchanging the positions of x and y in x=Φ(y); (3) Domain of inversion function (general) The definition domain of the inverse function can be obtained by the method of evaluating the range of the original function).