Question Number 4946 by FilupSmith last updated on 25/Mar/16
$$\mathrm{Lets}\:\mathrm{say}\:{y}={f}\left({x}\right):\forall{x}\in\mathbb{R},{y}\in\mathbb{R} \\ $$$$ \\ $$$$\mathrm{if}\:{a}=\mathrm{constent} \\ $$$$\mathrm{Does}\:\mathrm{there}\:\mathrm{exist}\:{f}\left({a}\right)={a} \\ $$$$\mathrm{for}\:\mathrm{any}\:\mathrm{function}\:{y}={f}\left({x}\right)? \\ $$$$\mathrm{Please}\:\mathrm{prove}/\mathrm{disprove} \\ $$
Commented by prakash jain last updated on 25/Mar/16
$${f}\left({x}\right)={x}\Rightarrow{f}\left({a}\right)={a} \\ $$