is-there-a-function-f-R-2-R-such-that-f-x-f-x-y-f-f-x-y-y-f-x-y-

Question Number 2514 by 123456 last updated on 21/Nov/15

$$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{function} \\ $$$${f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$${f}\left[{x},{f}\left({x},{y}\right)\right]={f}\left[{f}\left({x},{y}\right),{y}\right]={f}\left({x},{y}\right) \\ $$$$? \\ $$

Answered by prakash jain last updated on 21/Nov/15

$${f}\left({x},{y}\right)={C}\:\mathrm{meets}\:\mathrm{all}\:\mathrm{conditions}.\:\mathrm{So}\:\mathrm{function}\:\mathrm{exists}. \\ $$

Commented by prakash jain last updated on 21/Nov/15

$${C}\:\mathrm{constant} \\ $$

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