(1)由1+m/1=2得m=1(2) f(x)=x+1/xf(-x)=-x-1/x=-(x+1/x)=-f(x)f(x)是奇函数(3)设x1>x2>1则x1-x2>0、x1x2>0f(x1)-f(x2)=x1+1/x1-x2-1/x2=x1-x2+1/x1-1/x2=(x1-x2)+(x2-x1)/(x1x2)=(x1-x2)(1-1/x1x2)>0即x1>x2∴f(x)在(1,+∞)上是增函数
(1)由1+m/1=2得m=1(2) f(x)=x+1/xf(-x)=-x-1/x=-(x+1/x)=-f(x)f(x)是奇函数(3)设x1>x2>1则x1-x2>0、x1x2>0f(x1)-f(x2)=x1+1/x1-x2-1/x2=x1-x2+1/x1-1/x2=(x1-x2)+(x2-x1)/(x1x2)=(x1-x2)(1-1/x1x2)>0即x1>x2∴f(x)在(1,+∞)上是增函数