设,x2-3x+1/(x+1)=k,
则x2-3x+1=kx+k
x2-(3+k)x+1-k=0,
方程有解
△=(3+k)^2-4(1-k)
=k^2+10k+5>=0
得k<=-5-2*根号5
或k>=-5+2*根号5
所以f(x)=x2-3x+1/(x+1)的值域(-∝,-5-2*根号5]及[-5+2*根号5,+∝)