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 $${x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}={u}\Rightarrow{x}=\frac{{u}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}{u}}…
Question Number 196619 by universe last updated on 28/Aug/23 Answered by cortano12 last updated on 28/Aug/23 $$\:\:\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}}} \\ $$$$\:\:\mathrm{f}\left(\mathrm{x}\right)=\:−\frac{\mathrm{1}}{\mathrm{x}} \\ $$$$\:\:\mathrm{f}\left(\mathrm{2}\right)+\mathrm{f}\left(\mathrm{3}\right)+\mathrm{f}\left(\mathrm{6}\right)\:=\:−\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{6}}\right)\:=\:\begin{array}{|c|}{−\mathrm{1}}\\\hline\end{array} \\ $$$$…
Question Number 196522 by Erico last updated on 26/Aug/23 $$\mathrm{Prove}\:\mathrm{that}\:\forall\mathrm{n}\in\mathbb{N} \\ $$$$\underset{\:\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}} \mathrm{ln}{t}\:\mathrm{dt}\:\leqslant\:\mathrm{ln}\left(\underset{\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}} {t}\:\mathrm{dt}\right) \\ $$ Answered by aleks041103 last updated on 26/Aug/23…
Question Number 196257 by mathlove last updated on 21/Aug/23 Answered by cortano12 last updated on 21/Aug/23 $$\:\:\mathrm{g}\left(\mathrm{x}\right)\:\Rightarrow\mathrm{m}\:=\:\mathrm{2}+\mathrm{b}\:\mathrm{and}\:\mathrm{passes}\:\mathrm{through} \\ $$$$\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\:\mathrm{1}+\mathrm{b}+\mathrm{c}\right) \\ $$$$\:\Rightarrow\mathrm{y}−\left(\mathrm{1}+\mathrm{b}+\mathrm{c}\right)=\:\left(\mathrm{2}+\mathrm{b}\right)\left(\mathrm{x}−\mathrm{1}\right) \\ $$$$\:\Rightarrow\mathrm{y}=\:\left(\mathrm{2}+\mathrm{b}\right)\mathrm{x}−\mathrm{2}−\mathrm{b}+\mathrm{1}+\mathrm{b}+\mathrm{c} \\ $$$$\:\Rightarrow\mathrm{y}=\:\left(\mathrm{2}+\mathrm{b}\right)\mathrm{x}+\mathrm{c}−\mathrm{1}…
Question Number 196246 by mathlove last updated on 20/Aug/23 Commented by mathlove last updated on 20/Aug/23 $${faind}\:{the}\:{value}\:{of} \\ $$$$\left({fog}^{−\mathrm{1}} {of}\right)_{\mathrm{4}} =? \\ $$ Answered by…
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…
Question Number 195391 by mathlove last updated on 01/Aug/23 $${f}^{\mathrm{2}} \left({x}\right)+\mathrm{2}{f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{15} \\ $$$${f}\left({x}\right)=? \\ $$ Answered by MM42 last updated on 01/Aug/23 $$\left({f}+\mathrm{1}\right)^{\mathrm{2}} ={x}^{\mathrm{2}}…
Question Number 194990 by anurup last updated on 21/Jul/23 $$\mathrm{I}{f}\:\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −{x}+\mathrm{1}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${f}\left(\mathrm{1971}\right)+{f}\left(\mathrm{2021}\right)+{f}\left(\mathrm{50}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 194896 by cortano12 last updated on 19/Jul/23 $$\:\:\:\:\:\:\:\cancel{ } \\ $$ Answered by AST last updated on 19/Jul/23 $$\left({x}^{\mathrm{2}} −{f}\left({x}\right)\right)^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{2}} {f}\left({x}\right)=\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} {f}\left({x}\right)…
Question Number 194688 by CrispyXYZ last updated on 13/Jul/23 $$\mathrm{find}\:\mathrm{all}\:\mathrm{function}\:{f}:\:\mathbb{R}\:\rightarrow\:\mathbb{R}\:\mathrm{such}\:\mathrm{that}\:\forall{x},\:{y}\in\mathbb{R}, \\ $$$${f}\left({x}−{f}\left({y}\right)\right)={f}\left({f}\left({y}\right)\right)+{xf}\left({y}\right)+{f}\left({x}\right)−\mathrm{1}. \\ $$ Answered by Tinku Tara last updated on 13/Jul/23 $${put}\:{x}={f}\left({y}\right) \\ $$$${f}\left(\mathrm{0}\right)={f}\left({x}\right)+{x}^{\mathrm{2}}…