作业帮已知函数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?
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![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?](/uploads/image/z/15165783-63-3.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dx%26%23178%3B%28x%E2%88%88%5B-2%2C2%5D%29%2Cg%28x%29%3Da%26%23178%3Bsin%282x%2B%CF%80%2F6%29%2B3a%28x%E2%88%88%5B0%2C%CF%80%2F2%5D%29%2C%26%238707%3Bx1%E2%88%88%5B-2%2C2%5D%2C%26%238704%3Bx2%E2%88%88%5B0%2C%CF%80%2F2%5D%2C%E4%BD%BF%E5%BE%97f%28x1%29%3Dg%28x2%29%E6%88%90%E7%AB%8B%2C%E5%88%99%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF%3F)
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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?
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