find-all-function-f-R-R-wich-verify-x-y-R-2-f-x-f-y-x-y-x-y-f-t-dt-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 36935 by maxmathsup by imad last updated on 07/Jun/18

find all function f R→R wich verify ∀(x,y)∈ R^2 f(x).f(y) =∫_(x−y) ^(x+y) f(t)dt .

$${find}\:{all}\:{function}\:{f}\:{R}\rightarrow{R}\:\:{wich}\:{verify} \\ $$$$\forall\left({x},{y}\right)\in\:{R}^{\mathrm{2}} \:\:\:{f}\left({x}\right).{f}\left({y}\right)\:=\int_{{x}−{y}} ^{{x}+{y}} \:{f}\left({t}\right){dt}\:. \\ $$

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