Question Number 151616 by mathdanisur last updated on 22/Aug/21
$$\mathrm{let}\:\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\boldsymbol{\lambda}+\mathrm{x}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{and}\:\:\boldsymbol{\lambda}\geqslant\frac{-\mathrm{3}}{\mathrm{4}} \\ $$$$\mathrm{solve}\:\mathrm{in}\:\mathbb{R}\:\:\:\mathrm{f}\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\right)\:\leqslant\:\mathrm{0} \\ $$
Commented by mr W last updated on 22/Aug/21
$${then}\:{solution}\:{is}\:{x}\geqslant\lambda \\ $$
Commented by mr W last updated on 22/Aug/21
$${please}\:{check}\:{the}\:{question}! \\ $$$${example}\:{for}\:\lambda=\mathrm{1}\:\Rightarrow{no}\:{solution} \\ $$
Commented by mathdanisur last updated on 22/Aug/21
$$\mathrm{Sorry}\:\mathrm{Ser},\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\lambda\:-\:\mathrm{x}}{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} } \\ $$
Commented by mathdanisur last updated on 22/Aug/21
$$\mathrm{Solutions}\:\mathrm{dear}\:\mathrm{Ser} \\ $$