设函数f(x)=(sinαx+cosαx)^2+2cos^2αx(α>0)的相邻两对称中心相距π|2(1)求f(x)在【0,π|2,】上的值域(2)若函数y=g(x)的图像与函数f(x)的图像关于直线x=π|2对称,求函数g(x)的单调增区间
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![设函数f(x)=(sinαx+cosαx)^2+2cos^2αx(α>0)的相邻两对称中心相距π|2(1)求f(x)在【0,π|2,】上的值域(2)若函数y=g(x)的图像与函数f(x)的图像关于直线x=π|2对称,求函数g(x)的单调增区间](/uploads/image/z/7634731-67-1.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3D%28sin%CE%B1x%2Bcos%CE%B1x%29%5E2%2B2cos%5E2%CE%B1x%28%CE%B1%3E0%29%E7%9A%84%E7%9B%B8%E9%82%BB%E4%B8%A4%E5%AF%B9%E7%A7%B0%E4%B8%AD%E5%BF%83%E7%9B%B8%E8%B7%9D%CF%80%7C2%281%29%E6%B1%82f%EF%BC%88x%EF%BC%89%E5%9C%A8%E3%80%900%2C%CF%80%7C2%2C%E3%80%91%E4%B8%8A%E7%9A%84%E5%80%BC%E5%9F%9F%EF%BC%882%EF%BC%89%E8%8B%A5%E5%87%BD%E6%95%B0y%3Dg%EF%BC%88x%EF%BC%89%E7%9A%84%E5%9B%BE%E5%83%8F%E4%B8%8E%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%9B%BE%E5%83%8F%E5%85%B3%E4%BA%8E%E7%9B%B4%E7%BA%BFx%3D%CF%80%7C2%E5%AF%B9%E7%A7%B0%2C%E6%B1%82%E5%87%BD%E6%95%B0g%EF%BC%88x%EF%BC%89%E7%9A%84%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B4)
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