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Category: Relation and Functions

find-f-x-if-f-x-x-2-1-x-x-1-

Question Number 196621 by universe last updated on 28/Aug/23 $$\mathrm{find}\:\:\mathrm{f}\left(\mathrm{x}\right)\:\:\mathrm{if} \\ $$$$\:\mathrm{f}\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right)\:=\:\frac{\mathrm{x}}{\mathrm{x}+\mathrm{1}} \\ $$ Answered by MM42 last updated on 28/Aug/23 $${x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}={u}\Rightarrow{x}=\frac{{u}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}{u}}…

Question-196619

Question Number 196619 by universe last updated on 28/Aug/23 Answered by cortano12 last updated on 28/Aug/23 $$\:\:\mathrm{f}\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\right)\:=\:−\frac{\mathrm{1}}{\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$$$\:\:\mathrm{f}\left(\mathrm{x}\right)=\:−\frac{\mathrm{1}}{\mathrm{x}} \\ $$$$\:\:\mathrm{f}\left(\mathrm{2}\right)+\mathrm{f}\left(\mathrm{3}\right)+\mathrm{f}\left(\mathrm{6}\right)\:=\:−\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{6}}\right)\:=\:\begin{array}{|c|}{−\mathrm{1}}\\\hline\end{array} \\ $$$$…

Question-196257

Question Number 196257 by mathlove last updated on 21/Aug/23 Answered by cortano12 last updated on 21/Aug/23 $$\:\:\mathrm{g}\left(\mathrm{x}\right)\:\Rightarrow\mathrm{m}\:=\:\mathrm{2}+\mathrm{b}\:\mathrm{and}\:\mathrm{passes}\:\mathrm{through} \\ $$$$\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\:\mathrm{1}+\mathrm{b}+\mathrm{c}\right) \\ $$$$\:\Rightarrow\mathrm{y}−\left(\mathrm{1}+\mathrm{b}+\mathrm{c}\right)=\:\left(\mathrm{2}+\mathrm{b}\right)\left(\mathrm{x}−\mathrm{1}\right) \\ $$$$\:\Rightarrow\mathrm{y}=\:\left(\mathrm{2}+\mathrm{b}\right)\mathrm{x}−\mathrm{2}−\mathrm{b}+\mathrm{1}+\mathrm{b}+\mathrm{c} \\ $$$$\:\Rightarrow\mathrm{y}=\:\left(\mathrm{2}+\mathrm{b}\right)\mathrm{x}+\mathrm{c}−\mathrm{1}…

find-the-domain-of-definition-of-this-function-for-t-0-1-x-x-2x-1-lnt-dt-ptiCantor-

Question Number 196023 by pticantor last updated on 16/Aug/23 $${find}\:{the}\:{domain}\:{of}\:{definition}\:{of}\:{this} \\ $$$$\left.{function}\:{for}\:{t}\in\right]\mathrm{0};\mathrm{1}\left[\right. \\ $$$$\:\:\:\:\:\boldsymbol{\rho}\left({x}\right)=\int_{{x}} ^{\mathrm{2}{x}} \frac{\mathrm{1}}{{lnt}}{dt} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{ptiCantor} \\ $$ Answered by sniper237 last updated…