The range of the square + 2x + 2 of the function y = x + 1 / X is
The range of y = (x + 1) / (X & # 178; + 2x + 2)
The method of finding Δ
(x²+2x+2)y=x+1
yx²+2yx+2y=x+1
yx²+(2y-1)x+(2y-1)=0
y≠0
And Δ = (2y-1) & # - 4Y (2y-1) & gt; = 0
(2y-1)(-2y-1)>=0
(2y-1)(2y+1)<=0
-1 / 2 & lt; = y & lt; = 1 / 2, and Y ≠ 0
When y = 0
-x-1=0
x=-1
Y = 0 holds
To sum up, the range is [- 1 / 2,1 / 2]
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