集合A={x -2≤x≤a},B={y y=2x=3,x∈A},C={y y=x05,x∈A},且C包含于B,则实数A的
问题描述:
集合A={x -2≤x≤a},B={y y=2x=3,x∈A},C={y y=x05,x∈A},且C包含于B,则实数A的
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 ≥ 1/2for 0≤ z≤ a^2a^2≤2a+3(a-3)(a+1)≤ 0-1≤...