Function properties: If the function f(x) satisfies: f(a+x)=f(b-x), then f(x) is symmetrical about the straight line x=(a+b)/2.

This question: f(4+x)=f(-x), then the symmetry axis of f(x) is x = 2；;

F(2)= 1, which is the lowest point of f(x);

Let f(0)=3, and we can get f (4) = 3 from symmetry; The minimum value of f(x) is 1 and the maximum value is 3;

Therefore, to make f(x) have the minimum value 1 on [0, m], the symmetry axis x=2 should be in the interval [0, m], and m should not exceed 4;

So: 2 ≤ m ≤ 4;

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