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