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例题show：已知函数f(x)=(4x~2-7)/(2-x),x∈[0,1] (Ⅰ)求f(x)的单调区间和值域；(Ⅱ)设a≥1,函数g(x)=x~3-3a~2x-2a,x∈[0,1]。若对于任意x_∈[0,1],总存在x_0∈[0,1],使得g(x_0)=f(x_1)成立,求a的取值范围。命题指向：本题主要考查函数的单调性、值域、集合的包含关系、解不等式等基础知识,以及逻辑思维能力、运算能力和综合应用数学知识解决问题的能力。(1)基本思路：
Example: show: Known function f (x) = (4x ~ 2-7) / (2-x), x ∈ [0, 1] (I) Find the monotonic interval and range of f (x); (II) Let a≥1, the function g(x)=x~3-3a~2x-2a, x∈[0,1]. If for any x_∈[0,1], there is always x_0∈[0,1] such that g(x_0)=f(x_1) holds, find the range of a. Propositional Pointing: This topic mainly examines the monotonicity of the function, the range of values, the inclusion relation of the set, the inequality of the solution, and other basic knowledge, as well as the ability of logical thinking, the ability to calculate, and the ability to comprehensively apply mathematical knowledge to solve problems. (1) Basic ideas: