会的请给出详细解答设非空集合A={x|-2≤x≤a},B={y|y=2x+3,x∈A},C={z|z=x2,x∈A},且B∩C＝C求a的范围谢
问题描述：
会的请给出详细解答设非空集合A={x|-2≤x≤a},B={y|y=2x+3,x∈A},C={z|z=x2,x∈A},且B∩C＝C求a的范围谢
答
A={x|-2≤x≤a},B={y|y=2x+3 } = {x| -1≤x≤ 2a+3 }C={z|z=x^2,x∈A}B∩C＝C=>C is subset of Bz = x^2 => 0≤z≤ 4 and 0≤ z≤ a^2for 0≤z≤ 4=> 2a+3 ≥ 4a ≥ 1/2for0≤ z≤ a^2a^2≤2a+3(a-3)(a+...