已知函数f(x)=x²(x∈[-2,2]),g(x)=a²sin(2x+π/6)+3a(x∈[0,π/2]),∃x1∈[-2,2],∀x2∈[0,π/2],使得f(x1)=g(x2)成立,则实数a的取值范围是?

已知函数f(x)=x²(x∈[-2,2]),g(x)=a²sin(2x+π/6)+3a(x∈[0,π/2]),
∃x1∈[-2,2],∀x2∈[0,π/2],使得f(x1)=g(x2)成立,则实数a的取值范围是?

x∈[0,π/2]
sin(2x+π/6)∈[-1/2,1]
g(x)=a²sin(2x+π/6)+3a∈[-a²/2+3a,a²+3a]
f(x)=x²(x∈[-2,2])
f(x)∈[0,4]
∃x1∈[-2,2],∀x2∈[0,π/2],使得f(x1)=g(x2)成立
即交集不为空
交集为空时
a²+3a