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第1点信息探究型XINXI TANJIUXING(★★★)必做1已知函数f(x)的图象在[a,b]上连续,定义:f_1(x)=min{f(t)|a≤t≤x}(x∈[a,b]),f_2(x)=max{f(t)|a≤t≤x}(x∈[a,b]),其中,min{f(x)|x∈D}表示函数f(x)在D上的最小值,max|f(x)|x∈D}表示函数f(x)在D上的最大值.若存在最小正整数k,使得f_2(x)-f_1(x)≤k·(x-a)对任意的x∈[a,b]成立,则称函数f(x)为[a,b]上的“k阶收缩函数”.(Ⅰ)若f(x)=cosx,x∈[0,π],试写出f_1(x),f_2(x)的表达式.
The first point of information inquiry type XINXI TANJIUXING (★ ★ ★) must be done 1 The image of the known function f (x) is continuous on [a, b], defining: f_1 (x) = min {f (X∈ [a, b]), f_2 (x) = max {f (t) | a≤t≤x} (x∈ [a, b]), where min {f ) | x∈D} represents the minimum value of f (x) on D, max | f (x) | x∈D} represents the maximum value of f (x) on D. If there exists a minimum positive integer k, (X) ≤ k · (xa) for any x∈ [a, b], then the function f (x) is called the "k-th shrinkage function on [a, b] (Ⅰ) If f (x) = cosx, x∈ [0, π], try to write out the expression of f_1 (x), f_2 (x).