f-x-f-y-f-x-f-y-x-y-R-f-R-R-f-x-

Question Number 1862 by 123456 last updated on 17/Oct/15

$${f}\left[{x}−{f}\left({y}\right)\right]={f}\left({x}\right)−{f}\left({y}\right),\forall\left({x},{y}\right)\in\mathbb{R} \\ $$$${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}\right)=? \\ $$

Answered by prakash jain last updated on 18/Oct/15

$${f}\left({x}\right)={x}\:\mathrm{is}\:\mathrm{one}\:\mathrm{solution}. \\ $$$$ \\ $$

Answered by Rasheed Soomro last updated on 19/Oct/15

$${More}\:{generally}\:{f}\left({x}\right)={x}+{c}\:\:{is}\:\:{a}\:\:{solution},{where}\:{c}\:{is}\:{a}\:{constant}. \\ $$

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