x<0時,(x^2+1)是減函數(shù),故√(x^2+1)是減函數(shù),而-x也是減函數(shù),所以F(x)是減函數(shù)；
x>=0時,
F(x)=√(x^2+1)-x][√(x^2+1)+x]/[√(x^2+1)+x]
=(x^2+1-x^2)/[√(x^2+1)+x]
=1/[√(x^2+1)+x]
因x>=0,分母中√(x^2+1),x都是增函數(shù),所以F(x)為減函數(shù)；
綜上,F(x)在R上都是減函數(shù).