Let g (x) be a function defined on R with period 1. If the value range of function f (x) = x + G (x) on interval [0,1] is [- 2,5], then the value range of F (x) on interval [0,3] is___ .

If G (x) is a function of period 1 on R, then G (x) = g (x + 1)
The value range of the function f (x) = x + G (x) in the interval [0,1] (exactly the length of a periodic interval) is [- 2,5] （1）
Let x + 1 = t,
When x ∈ [0,1], t = x + 1 ∈ [1,2]
In this case, f (T) = t + G (T) = (x + 1) + G (x + 1) = (x + 1) + G (x) = [x + G (x)] + 1
Therefore, when t ∈ [1,2], f (T) ∈ [- 1,6] （2）
Let x + 2 = t,
When x ∈ [0,1], t = x + 2 ∈ [2,3]
In this case, f (T) = t + G (T) = (x + 2) + G (x + 2) = (x + 2) + G (x) = [x + G (x)] + 2
Therefore, when t ∈ [2,3], f (T) ∈ [0,7] （3）
According to the known conditions and (1) (2) (3), the value range of F (x) on the interval [0,3] is [- 2,7]
So the answer is: [- 2, 7]

Let g (x) be a function defined on R with period 1. If the value range of function f (x) = x + G (x) on the interval [34] is [- 25], then the value range of F (x) on the interval [- 10 10] is?

The reason is very simple. The value range of F (x) on the interval [- 10 - 9] is [- 15 - 8], and that on the interval [910] is [411]. Therefore, the value range of F (x) on the interval [- 1010] is [- 1511]

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Let g (x) be a function defined on R with period 1. If the value range of function f (x) = x + G (x) on interval [0,1] is [- 2,5], then the value range of F (x) on interval [0,3] is___ .