f(x)定义域【0,1】f(0)=0,f(1)=1,x>=y时有f(x+y的和/2)=f(x)sina+(1-sina)f(y) a属于(0,π/2)
问题描述:
f(x)定义域【0,1】f(0)=0,f(1)=1,x>=y时有f(x+y的和/2)=f(x)sina+(1-sina)f(y) a属于(0,π/2)
求f(1/2),f(1/4),a的值
答
f(1/2)=f(1)sina+(1- sina)f(0)=sina,
f(1/4)=f(1/2)sina+(1- sina)f(0)=(sina)^2,