【急在线等】设a∈(0,π/2),函数f(x)的定义域为[0,1],且f(0)=0,f(1)=1,设a∈(0,π/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),求:(1)f(1/2),f(1/4)(2)α的值(3)函
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![【急在线等】设a∈(0,π/2),函数f(x)的定义域为[0,1],且f(0)=0,f(1)=1,设a∈(0,π/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),求:(1)f(1/2),f(1/4)(2)α的值(3)函](/uploads/image/z/14796057-57-7.jpg?t=%E3%80%90%E6%80%A5%E5%9C%A8%E7%BA%BF%E7%AD%89%E3%80%91%E8%AE%BEa%E2%88%88%280%2C%CF%80%2F2%29%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%3D0%2Cf%281%29%3D1%2C%E8%AE%BEa%E2%88%88%280%2C%CF%80%2F2%29%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%3D0%2Cf%281%29%3D1%2C%E5%BD%93x%E2%89%A5y%E6%97%B6%2C%E6%9C%89f%28%28x%2By%29%2F2%29%3Df%28x%29%2Asin%CE%B1%2B%281-+sin%CE%B1%29%2Af%28y%29%2C%E6%B1%82%EF%BC%9A%EF%BC%881%EF%BC%89f%281%2F2%29%2Cf%281%2F4%29%EF%BC%882%EF%BC%89%CE%B1%E7%9A%84%E5%80%BC%EF%BC%883%EF%BC%89%E5%87%BD)
【急在线等】设a∈(0,π/2),函数f(x)的定义域为[0,1],且f(0)=0,f(1)=1,设a∈(0,π/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),求:(1)f(1/2),f(1/4)(2)α的值(3)函
【急在线等】设a∈(0,π/2),函数f(x)的定义域为[0,1],且f(0)=0,f(1)=1,
设a∈(0,π/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),求:
(1)f(1/2),f(1/4)
(2)α的值
(3)函数g(x)=sin(α-2x)的单调递增区间
【急在线等】设a∈(0,π/2),函数f(x)的定义域为[0,1],且f(0)=0,f(1)=1,设a∈(0,π/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),求:(1)f(1/2),f(1/4)(2)α的值(3)函
(1)f(1/2)=f((0+1)/2)
=f(0)*sinα+(1-sinα)*f(1)
=1-sinα
又f(1/2)=f((1+0)/2)
=f(1)*sinα+(1-sinα)*f(0)
=sinα
所以1-sinα=sinα sinα=1/2
故f(1/2)=sinα=1/2
同理f(1/4)=f((0+1/2)/2)=f(0)*sinα+(1-sinα)*f(1/2)
=(1/2)*(1/2)=1/4
(2)由(1)知sinα=1/2
又a∈(0,π/2)
所以a=π/6
(3)g(x)=sin(α-2x)=sin(π/6-2x)
=-sin(2x-π/6)
求函数g(x)=sin(α-2x)的单调递增区间就是求函数sin(2x-π/6)的单调递减区间
则2kπ+π/2<2x-π/6