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let-f-x-x-1-x-2-and-3-4-solve-in-R-f-f-f-x-0-




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

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