设A={x|-2≤x≤a},B={y|y=2x+3,x∈A},C={z|z=x^2,x∈A},且C含于B,求实数a的取值范围
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![设A={x|-2≤x≤a},B={y|y=2x+3,x∈A},C={z|z=x^2,x∈A},且C含于B,求实数a的取值范围](/uploads/image/z/11422212-60-2.jpg?t=%E8%AE%BEA%3D%7Bx%7C-2%E2%89%A4x%E2%89%A4a%7D%2CB%3D%7By%7Cy%3D2x%2B3%2Cx%E2%88%88A%7D%2CC%3D%7Bz%7Cz%3Dx%5E2%2Cx%E2%88%88A%7D%2C%E4%B8%94C%E5%90%AB%E4%BA%8EB%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
设A={x|-2≤x≤a},B={y|y=2x+3,x∈A},C={z|z=x^2,x∈A},且C含于B,求实数a的取值范围
设A={x|-2≤x≤a},B={y|y=2x+3,x∈A},C={z|z=x^2,x∈A},且C含于B,求实数a的取值范围
设A={x|-2≤x≤a},B={y|y=2x+3,x∈A},C={z|z=x^2,x∈A},且C含于B,求实数a的取值范围
A={x|-2≤x≤a},
B={y|y=2x+3,x∈A}
y=2x+3,递增,-2≤x≤a
∴-1≤y≤2a+3
∴B={y|-1≤y≤2a+3}
C={z|z=x²,x属于A}
z=x²,-2≤x≤a
∴z的最大值是当x=-2或x=a时取得
∵C包含于B
∴x=-2时,z=4≤2a+3 ==> a≤1/2
x=a时,z=a²≤2a+3 ==> a²-2a-3 ≤0 ==> -1≤a≤3
∴实数a的取值范围是-1≤a≤1/2