At a function

Algebra Level 3

Assume that 2A(x)=exex2A(x)=e^x-e^{-x} and A(B(x))=xA \left( B(x) \right) =x, find the value of B(e289012e1445).B \left( \dfrac{e^{2890}-1}{2 e^{1445}}\right).

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