f(x)=2x/(x²+1)
=2/(x+1/x) .上下同时除以x
∵x+1/x≥2√(x×1/x)=2
∴0＜1/(x+1/x)≤1/2
∴0＜f(x)≤1
∴f(x)的值域为(0,1]