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Question

Let f:RR be a continuous odd function, which vanishes exactly at one point and f(1)=12 . Suppose that F(x)=x1f(t)dt for all x[1,2] and G(x)=x1t|f(f(t))|dt for all x[1,2] .
If limx1F(x)G(x)=114 , then the value of f(12)

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