Question Number 1970 by 123456 last updated on 27/Oct/15
![f:[0,+∞)→R xf(x)=f[f(x)]f(x) f(x)=?](Q1970.png)
$${f}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R} \\ $$$${xf}\left({x}\right)={f}\left[{f}\left({x}\right)\right]{f}\left({x}\right) \\ $$$${f}\left({x}\right)=? \\ $$
Answered by prakash jain last updated on 27/Oct/15
$${f}\left({x}\right)\neq\mathrm{0}\:\mathrm{then}\:{f}\left({f}\left({x}\right)={x}\right. \\ $$$$\mathrm{The}\:\mathrm{following}\:\mathrm{are}\:\mathrm{also}\:\mathrm{solutions} \\ $$$${f}\left({x}\right)=\left({k}−{x}^{{n}} \right)^{\mathrm{1}/{n}} \Rightarrow{f}\left({f}\left({x}\right)\right)={x} \\ $$$${f}\left({x}\right)=\frac{{k}}{{x}}\Rightarrow{f}\left({f}\left({x}\right)\right)={x} \\ $$$${more}\:{solutions}\:{will}\:{also}\:{be}\:{therr} \\ $$
Answered by Rasheed Soomro last updated on 27/Oct/15
$${One}\:{solution}\:{is}\:{f}\left({x}\right)={x} \\ $$