F (x) domain R. satisfies f (x + 1) [1-f (x)] = 1 + F (x). Proof: F (x) is a periodic function It has been proved that the period is 2 Problem 1, when x belongs to [0,1], f (x) = x, find the expression of F (x) on [- 1,0] 2. For the function f (x) = ax in 1 with 100 roots, find the value range of A PS steps, direct answers do not give points

F (x) domain R. satisfies f (x + 1) [1-f (x)] = 1 + F (x). Proof: F (x) is a periodic function It has been proved that the period is 2 Problem 1, when x belongs to [0,1], f (x) = x, find the expression of F (x) on [- 1,0] 2. For the function f (x) = ax in 1 with 100 roots, find the value range of A PS steps, direct answers do not give points

1. Let x ∈ [- 1,0), then x + 1 ∈ [0,1], f (x + 1) = x + 1
Because f (x + 1) [1-f (x)] = 1 + F (x)
So (x + 1) [1-f (x)] = 1 + F (x)
f(x)=x/(x+2)

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