设x1<x2,则x2-x1>0,
∴0<f(x2-x1)<1,
∴f(x2)-f(x1)
=f[(x2-x1)+x1]-f(x1)
=f(x2-x1)f(x1)-f(x1)
=f(x1)[f(x2-x1)-1]<0,
∴f(x)在R上单调递减.