y=(x^2+2x+2)/(x+1)
=((x+1)^2+1)/(x+1)
=(x+1)+1/(x+1)
x+1>0时,(x+1)+1/(x+1)≥2√[(x+1)*1/(x+1)]=2,
x+1<0时,-(x+1) >0,
-(x+1)-1/(x+1)≥2√[-(x+1)*-1/(x+1)]=2,
所以(x+1)+1/(x+1)≤-2.
函数值域是（-∞,-2]∪[2,+∞）.x+1>0时，(x+1)+1/(x+1)≥2√[(x+1)*1/(x+1)]=2,为什么大于等于号后面有根号这里利用的是基本不等式：a+b≥2√(ab),后面当然有根号。