已知f(x)=-2asin(2x+π/6)+2a+b,x∈[π/4,3π/4],是否存在常数a,b∈Q(有理数)时,使得f(x)的值域为[-3,根3-1]?若存在,求出a,b的值;若不存在,说明理由.以上两个区间均为闭区间~
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![已知f(x)=-2asin(2x+π/6)+2a+b,x∈[π/4,3π/4],是否存在常数a,b∈Q(有理数)时,使得f(x)的值域为[-3,根3-1]?若存在,求出a,b的值;若不存在,说明理由.以上两个区间均为闭区间~](/uploads/image/z/5551265-65-5.jpg?t=%E5%B7%B2%E7%9F%A5f%28x%29%3D-2asin%282x%2B%CF%80%2F6%29%2B2a%2Bb%2Cx%E2%88%88%5B%CF%80%2F4%2C3%CF%80%2F4%5D%2C%E6%98%AF%E5%90%A6%E5%AD%98%E5%9C%A8%E5%B8%B8%E6%95%B0a%2Cb%E2%88%88Q%EF%BC%88%E6%9C%89%E7%90%86%E6%95%B0%EF%BC%89%E6%97%B6%2C%E4%BD%BF%E5%BE%97f%28x%29%E7%9A%84%E5%80%BC%E5%9F%9F%E4%B8%BA%5B-3%2C%E6%A0%B93-1%5D%3F%E8%8B%A5%E5%AD%98%E5%9C%A8%2C%E6%B1%82%E5%87%BAa%2Cb%E7%9A%84%E5%80%BC%EF%BC%9B%E8%8B%A5%E4%B8%8D%E5%AD%98%E5%9C%A8%2C%E8%AF%B4%E6%98%8E%E7%90%86%E7%94%B1.%E4%BB%A5%E4%B8%8A%E4%B8%A4%E4%B8%AA%E5%8C%BA%E9%97%B4%E5%9D%87%E4%B8%BA%E9%97%AD%E5%8C%BA%E9%97%B4%7E)
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