x1>x2>=1
f(x1)-f(x2)
=x1+1/x1-x2-1/x2
=(x1²x2-x1x2²+x2-x1)/x1x2
=(x1-x2)(x1x2-1)/x1x2
x1>x2>=1
所以x1-x2>0
x1x2>1则x1x2-1>0
x1x2>0
所以f(x1)-f(x2)>0
即x1>x2>=1时f(x1)>f(x2)
所以是增函数