f-x-function-pair-and-0-decreases-in-the-range-f-x-f-3-solve-the-inequality-

Question Number 127322 by MathSh last updated on 28/Dec/20

$${f}\left({x}\right)\:{function}\:{pair}\:{and}\:\left(−\infty;\mathrm{0}\right] \\ $$$${decreases}\:{in}\:{the}\:{range} \\ $$$${f}\left({x}\right)\geqslant{f}\left(−\mathrm{3}\right)\:{solve}\:{the}\:{inequality} \\ $$

Answered by mindispower last updated on 28/Dec/20

$$\left.\right]\left.−\infty,−\mathrm{3}\right]\cup\left[\mathrm{3},+\infty\left[\right.\right. \\ $$$$ \\ $$

Commented by MathSh last updated on 28/Dec/20

$${Solution}\:{sir}\:{pliz} \\ $$

Commented by mindispower last updated on 28/Dec/20

$${since}\:{f}\:{decrease} \\ $$$$\left.{i}\left.{n}\:\right]−\infty,\mathrm{0}\right]\Rightarrow\forall{x}\leqslant−\mathrm{3},{f}\left({x}\right)\geqslant{f}\left(−\mathrm{3}\right) \\ $$$$\left.\Rightarrow\left.{x}\in\right]−\infty,−\mathrm{3}\right]\:{is}\:{solution} \\ $$$${f}\left({x}\right)={f}\left(−{x}\right)\:{f}\:{est}\:{une}\:{fonction}\:{paire} \\ $$$$\Rightarrow\left[\mathrm{3},\infty\right]\:{est}\:{aussi}\:{solution} \\ $$$$\left.\right]\left.−\infty,−\mathrm{3}\right]\cup\left[\mathrm{3},\infty\left[\:{sont}\:{solution}\right.\right. \\ $$$${mais}\:{pas}\:{que}\:{car}\:{f}\:{peut}\:{etre}\:{constante}\:{sur}\: \\ $$$$\left[−\mathrm{3},\mathrm{3}\right]\:{dans}\:{ce}\:{cas}\:{S}=\mathbb{R}\: \\ $$$${exemple}\:{f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{2}} ,{x}\in\mathbb{R}−\left[−\mathrm{3},\mathrm{3}\right]}\\{\mathrm{9}\:{si}\:{x}\in\left[−\mathrm{3},\mathrm{3}\right]}\end{cases}\: \\ $$$${f}\left({x}\right)\geqslant{f}\left(−\mathrm{3}\right),\:{les}\:{solution}\:{sont}\:\mathbb{R}\:{tous}\:{entier} \\ $$$$ \\ $$

Terms of Service
Privacy Policy
Contact: info@tinkutara.com