Question

当x>-1时,求f(x)=x2-3x+1/(x+1)的值域

Answer 1

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

所以f(x)=x2-3x+1/(x+1)的值域(-∝,-5-2*根号5]及[-5+2*根号5,+∝)