f(x)在[1,+∞)上单调递增.
证：
设1≤x1x1 x2>1 x2²-1>0 √(x2²-1)]>0
√(x2²-1)+√(x1²-1)>0
x2>0 x1>0 x2+x1>0
x2>x1 x2-x1>0
(x2+x1)(x2-x1)/[√(x2²-1)+√(x1²-1)]>0
f(x2)-f(x1)>0
f(x2)>f(x1)
f(x)在[1,+∞)上单调递增.