y=(x+1)/(x^2+2x+2)
分母配方y=(x+1)/[(x+1)^2+1]
x=-1, x+1=0, y=0
x+1不等于0时分子分母同顷州除（x+1)
y=1/[(x+1)+1/(x+1)]
分母使用均值定理(x+1分正负讨雀局蔽论)
(x+1)+1/(x+1)小于等于-2或大于等于2
x+1不等于0时，y值域{y|-1/2<=y<=1/2, 且y不等于0}
综上腊吵所述，函数值域[-1/2,1/2]
函数y等于x+1/x的平方+2x+2的值域是多少
y=(x+1)/(x^2+2x+2)
分母配方y=(x+1)/[(x+1)^2+1]
x=-1, x+1=0, y=0
x+1不等于0时分子分母同顷州除（x+1)
y=1/[(x+1)+1/(x+1)]
分母使用均值定理(x+1分正负讨雀局蔽论)
(x+1)+1/(x+1)小于等于-2或大于等于2
x+1不等于0时，y值域{y|-1/2<=y<=1/2, 且y不等于0}
综上腊吵所述，函数值域[-1/2,1/2]