Question Number 184942 by mnjuly1970 last updated on 14/Jan/23 $$ \\ $$$$\:\:\:\:{f}\left({x}\:\right)=\:{x}\:+\:\lfloor\:\:{x}\:+\:\frac{\:\lfloor\:\:\underset{} {\overset{} {{x}}}\:\:\rfloor}{\lfloor\:\:\:\frac{{x}^{\:\mathrm{2}} }{\mathrm{1}\:+{x}^{\:\mathrm{2}} }\:\:\:\rfloor+\mathrm{1}}\:\rfloor \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:{f}^{\:−\mathrm{1}} \:\left({x}\:\right)=? \\ $$ Commented by Frix last…
Question Number 184941 by a.lgnaoui last updated on 14/Jan/23 $${Determiner}\:{une}\:{relation}\:{entre} \\ $$$${les}\:{coeficients}\:{de}\:{x},{y},{z}\: \\ $$$${pour}\:{que}\:\:{z}={x}+{y} \\ $$$$ \\ $$$${a}_{\mathrm{1}} {x}+{b}_{\mathrm{1}} {y}+{c}_{\mathrm{1}} {z}={u} \\ $$$${a}_{\mathrm{2}} {x}+{b}_{\mathrm{2}} {y}+{c}_{\mathrm{2}}…
Question Number 184938 by mnjuly1970 last updated on 14/Jan/23 $$ \\ $$$$\:\:\:\:\:\mathrm{If}\:\:,\:\:\begin{cases}{\:\:{f}\:\::\:\:\left[\:\sqrt{\mathrm{2}}\:,\:+\infty\:\right)\:\rightarrow\:\mathbb{R}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\\{\:\:\:{f}\:\left({x}\:\right)\:=\:{x}^{\:\mathrm{2}} \:\:+\:\lfloor\:\frac{\:\mathrm{1}}{\mathrm{1}\:−\:\lfloor\:{x}^{\:\mathrm{2}} \:\rfloor}\:\rfloor\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\:\lfloor\:\:{f}^{\:−\mathrm{1}} \:\left(\:\pi\:\right)\:\rfloor\:=\:? \\ $$$$ \\ $$$$ \\ $$…
Question Number 119396 by bemath last updated on 24/Oct/20 $${If}\:{the}\:{roots}\:{of}\:{the}\:{equation}\: \\ $$$$\mathrm{24}{x}^{\mathrm{4}} −\mathrm{52}{x}^{\mathrm{3}} +\mathrm{18}{x}^{\mathrm{2}} +\mathrm{13}{x}−\mathrm{6}=\mathrm{0}\:{are}\: \\ $$$$\alpha\:,\:−\alpha\:,\:\beta\:{and}\:\frac{\mathrm{1}}{\beta}.\:{Find}\:{the}\:{value}\:{of}\: \\ $$$$\alpha\:{and}\:\beta. \\ $$ Commented by Dwaipayan Shikari…
Question Number 184927 by mathlove last updated on 14/Jan/23 $${s}=\frac{\mathrm{2}}{\mathrm{11}^{\mathrm{0}} }+\frac{\mathrm{6}}{\mathrm{11}}+\frac{\mathrm{10}}{\mathrm{11}^{\mathrm{2}} }+\frac{\mathrm{14}}{\mathrm{11}^{\mathrm{3}} }+\frac{\mathrm{18}}{\mathrm{11}^{\mathrm{4}} }+\centerdot\centerdot\centerdot\centerdot \\ $$$${s}=? \\ $$ Answered by Rasheed.Sindhi last updated on 14/Jan/23…
Question Number 53842 by Tawa1 last updated on 26/Jan/19 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{real}\:\mathrm{valued}\:\:\mathrm{f}\:\:\mathrm{satisfying}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{f}\left[\mathrm{2x}\:+\:\mathrm{f}\left(\mathrm{2y}\right)\right]\:+\:\mathrm{f}\left[\mathrm{f}\left(\mathrm{y}\right)\right]\:\:=\:\:\mathrm{4x}\:+\:\mathrm{8y} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{real}\:\mathrm{numbers}\:\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}.\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 184914 by Linton last updated on 13/Jan/23 $$ \\ $$ Lindsey randomly selects 2 distinct days each lveek to go to the gym.…
Question Number 53827 by Mikael_Marshall last updated on 26/Jan/19 $$\mathrm{5}×\mathrm{6}^{{x}} −\mathrm{3}×\mathrm{4}^{{x}} =\:\mathrm{2}×\mathrm{9}^{{x}} \\ $$$$ \\ $$$${I}\:{need}\:{an}\:{explanation}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 26/Jan/19…
Question Number 184893 by mnjuly1970 last updated on 13/Jan/23 $$ \\ $$$$\:\:\:\:{find}\:{the}\:{set}\:{of}\: \\ $$$$\:\:\:\:{critical}\:{points}\:{for}: \\ $$$$\:\:\:\mathrm{1}:\:\:\:{f}\:\left({x}\right)\:=\:\frac{{x}}{\lfloor\:{x}\:\rfloor+\lfloor\:−{x}\rfloor}\:−{x}\:\:\:\: \\ $$$$\:\:\:\:\mathrm{2}\::\:\:{g}\left({x}\right)\:=\:\frac{{x}}{\lfloor\:{x}\:\rfloor\:+\lfloor\:−{x}\:\rfloor}\:+{x} \\ $$ Answered by Mathspace last updated…
Question Number 184877 by Shrinava last updated on 13/Jan/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{last}\:\mathrm{ten}\:\mathrm{digits}: \\ $$$$\mathrm{5}^{\mathrm{23}} \:\centerdot\:\mathrm{2}^{\mathrm{2022}} \:−\:\mathrm{2023} \\ $$ Answered by Rasheed.Sindhi last updated on 14/Jan/23 $$\mathrm{5}^{\mathrm{23}} \:\centerdot\:\mathrm{2}^{\mathrm{2022}}…