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问题: 高二数学题求助,快~

求下列函数的值域.
1.y=x+1/x (x≠0)
2.y=(x-1)/(x+1) (x≠-1)
3.y=x/(x²+1)
4.y=x²+1/(x²+2)

解答:

1. y=x+1/x (x≠0)
x>0: y=x+1/x>=2;x<0: -y=(-x)+1/(-x)>=2, y<=-2
==> 值域: y<=-2, y>=2
2. y=(x-1)/(x+1) (x≠-1)
x=-(y+1)/(y-1) ==> 值域: y≠1
3. y=x/(x²+1) =1/(x +1/x)
由(1),有, 值域: -1/2<=y<=1/2
4. y=x²+1/(x²+2) =(x²+2) +1/(x²+2) -1 >= 2 -1 =1
值域: y>=1