数学题当x>-1时,求f(x)=(x^2-3x+1)/(x+1)的值域

题目

数学题当x>-1时,求f(x)=(x^2-3x+1)/(x+1)的值域

答案

f(x)=[(x+1)(x-4)+5]/(x+1)
=x-4+5/(x+1)
=(x+1)+5/(x+1)+5
x>-1
x+1>0
f(x)≥2√[(x+1)*5/(x+1)]+5=2√5+5
值域[2√5+5,正无穷)