设α∈(0,Pi/2 ),函数f(x)的定义域为[0,1],且f(0) = 0,f(1) =1,当x≥ y时,有f((x+y)/2 )= f(x)sinα+ (1- sinα)f(y).(1)求f(1/2 )、f(1/4 );(2)求α的值.
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![设α∈(0,Pi/2 ),函数f(x)的定义域为[0,1],且f(0) = 0,f(1) =1,当x≥ y时,有f((x+y)/2 )= f(x)sinα+ (1- sinα)f(y).(1)求f(1/2 )、f(1/4 );(2)求α的值.](/uploads/image/z/1136074-58-4.jpg?t=%E8%AE%BE%CE%B1%E2%88%88%EF%BC%880%2CPi%2F2+%EF%BC%89%2C%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BA%5B0%2C1%5D%2C%E4%B8%94f%280%29+%3D+0%2Cf%281%29+%3D1%2C%E5%BD%93x%E2%89%A5+y%E6%97%B6%2C%E6%9C%89f%EF%BC%88%28x%2By%29%2F2+%EF%BC%89%3D+f%28x%29sin%CE%B1%2B+%281-+sin%CE%B1%29f%28y%29%EF%BC%8E%EF%BC%881%EF%BC%89%E6%B1%82f%281%2F2+%29%E3%80%81f%281%2F4+%29%EF%BC%9B%EF%BC%882%EF%BC%89%E6%B1%82%CE%B1%E7%9A%84%E5%80%BC.)
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