当x=0时,f(x)=0
当x>0时,
f(x)=(2x)/(x^2+1) =2/(x+1/x)
x+1/x>=2,所以2/(x+1/x)0,所以2/(x+1/x)>0
所以f(x)属于(0,1]
综上所述,f(x)属于[0,1],即f(x)=(2x)/(x^2+1) ---- (x≥0) 的值域为[0,1]
当x=0时,f(x)=0
当x>0时,
f(x)=(2x)/(x^2+1) =2/(x+1/x)
x+1/x>=2,所以2/(x+1/x)0,所以2/(x+1/x)>0
所以f(x)属于(0,1]
综上所述,f(x)属于[0,1],即f(x)=(2x)/(x^2+1) ---- (x≥0) 的值域为[0,1]