Find-all-the-real-valued-f-satisfying-f-2x-f-2y-f-f-y-4x-8y-for-all-real-numbers-x-and-y-

Question Number 53842 by Tawa1 last updated on 26/Jan/19

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{real}\:\mathrm{valued}\:\:\mathrm{f}\:\:\mathrm{satisfying}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{f}\left[\mathrm{2x}\:+\:\mathrm{f}\left(\mathrm{2y}\right)\right]\:+\:\mathrm{f}\left[\mathrm{f}\left(\mathrm{y}\right)\right]\:\:=\:\:\mathrm{4x}\:+\:\mathrm{8y} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{real}\:\mathrm{numbers}\:\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}.\: \\ $$

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