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Answer to Question #22765 in Abstract Algebra for ekra

Question #22765
Let F be an additive group of all continuous functions mapping IR into IR. Let IR be the additive group of real numbers, and let ф :F ------> IR be given by ф(f) = ∫_0^4▒〖f(x)dx〗 . Prove that f is a homomorphism?
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