The range of function f (x) = (X & # 178; + X + 1) / (X & # 178; + 1) is

f(x)=（x^2+x+1）/（x^2+1）
Let = (x ^ 2 + X + 1) / (x ^ 2 + 1) = t
x^2+x+1= t（x^2+1）
(t-1)x^2-x+(t-1)=0
Discriminant = (- 1) ^ 2-4 (t-1) ^ 2 ≥ 0
（t-1)^2≤1/4
-1/2≤t-1≤1/2
1/2≤t≤3/2
Range [1 / 2,3 / 2]

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