求函数y=x²-2x+1/x²+1的值域

求函数y=x²-2x+1/x²+1的值域
求函数y=x²-2x+1/x²+1的值域

求函数y=x²-2x+1/x²+1的值域
y = (x^2-2x+1)/(x^2+1)
y' = [ (x^2+1)(2x-2)-2x(x^2-2x+1) ] /(x^2+1)^2
= (2x^2-2)/(x^2+1)^2
y' = 0
x= 1 (min) or -1 (max)
max y = y(-1)
=2
miny = y(1) =0
值域=[0,2]