Question Number 2514 by 123456 last updated on 21/Nov/15
![is there a function f:R^2 →R such that f[x,f(x,y)]=f[f(x,y),y]=f(x,y) ?](Q2514.png)
$$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{function} \\ $$$${f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$${f}\left[{x},{f}\left({x},{y}\right)\right]={f}\left[{f}\left({x},{y}\right),{y}\right]={f}\left({x},{y}\right) \\ $$$$? \\ $$
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
$${C}\:\mathrm{constant} \\ $$