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
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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
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 B
z = x^2 => 0≤z≤ 4 and 0≤ z≤ a^2
for 0≤z≤ 4
=> 2a+3 ≥ 4
a ≥ 1/2
for 0≤ z≤ a^2
a^2≤2a+3
(a-3)(a+1)≤ 0
-1≤a≤3
-1≤a≤3 and a ≥ 1/2
=> 1/2≤a≤3
B={y|y=2x+3 }
= {x| -1≤x≤ 2a+3 }
C={z|z=x^2,x∈A}
B∩C=C => C is subset of B
z = x^2 => 0≤z≤ 4 and 0≤ z≤ a^2
for 0≤z≤ 4
=> 2a+3 ≥ 4
a ≥ 1/2
for 0≤ z≤ a^2
a^2≤2a+3
(a-3)(a+1)≤ 0
-1≤a≤3
-1≤a≤3 and a ≥ 1/2
=> 1/2≤a≤3
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