Question Number 87535 by mathmax by abdo last updated on 04/Apr/20 $${let}\:{U}_{{n}} =\left\{{z}\in{C}\:/{z}^{{n}} =\mathrm{1}\right\} \\ $$$${calculate}\:\sum_{{k}=\mathrm{0}\:{and}\:{z}\in{U}_{{n}} } ^{{p}−\mathrm{1}} \:{z}^{{k}} \\ $$ Terms of Service Privacy…
Question Number 87530 by mathmax by abdo last updated on 04/Apr/20 $$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{e}^{−{n}\left[{x}\right]} {sin}\left(\frac{\pi{x}}{{n}}\right){dx}\:\:{nnatural}\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right){determine}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Commented by mathmax by abdo…
Question Number 87464 by jagoll last updated on 04/Apr/20 $$\mathrm{x}\:+\:\sqrt{\mathrm{y}}\:=\:\mathrm{7} \\ $$$$\sqrt{\mathrm{x}}\:+\:\mathrm{y}\:=\:\mathrm{11}\: \\ $$$$\mathrm{find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\: \\ $$ Commented by john santu last updated on 04/Apr/20 $$\mathrm{y}\:=\:\mathrm{9}\:\wedge\:\mathrm{x}\:=\:\mathrm{4}…
Question Number 87459 by john santu last updated on 04/Apr/20 $$\mathrm{find}\:\mathrm{all}\:\mathrm{functions}\:\mathrm{f}\::\mathbb{R}\:\rightarrow\mathbb{R} \\ $$$$\mathrm{so}\:\mathrm{that}\:\left(\mathrm{x}−\mathrm{y}\right)\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)\:−\left(\mathrm{x}+\mathrm{y}\right)\:\mathrm{f}\left(\mathrm{x}−\mathrm{y}\right)\:= \\ $$$$\mathrm{4xy}\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \right)\:\forall\mathrm{x},\mathrm{y}\:\in\mathbb{R} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 87352 by jagoll last updated on 04/Apr/20 $$\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)\:−\mathrm{x} \\ $$$$\mathrm{f}\left(\mathrm{0}\right)=\:\mathrm{123} \\ $$$$\mathrm{f}\left(\mathrm{29}\right)\:=? \\ $$ Commented by jagoll last updated on 04/Apr/20 $$\mathrm{x}=\mathrm{0}\:\Rightarrow\:\mathrm{123}=\mathrm{f}\left(\mathrm{1}\right)−\mathrm{0} \\…
Question Number 152799 by nadovic last updated on 01/Sep/21 $$\:\:\mathrm{Given}\:\mathrm{that}\:{f}\circ{g}\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}{x}^{\mathrm{2}} \:−\:{x}\:+\:\mathrm{4}}\:\:\mathrm{and} \\ $$$$\:\:{g}\left({x}\right)\:=\:\frac{{x}}{{x}\:−\:\mathrm{2}},\:\mathrm{find}\:{f}\left({x}\right). \\ $$ Commented by otchereabdullai@gmail.com last updated on 08/Sep/21 $$\mathrm{nice}! \\…
Question Number 152769 by liberty last updated on 01/Sep/21 Commented by mathdanisur last updated on 01/Sep/21 $$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{x}}{\mathrm{2}}+\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{3}}{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \\ $$ Answered by tabata last…
Question Number 21692 by Joel577 last updated on 01/Oct/17 $$\mathrm{Let}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{equation}\:\mathrm{and} \\ $$$${x}^{\mathrm{2}} \:−\:\mathrm{2}{x}\:+\:\mathrm{3}\:\leqslant\:{f}\left({x}\right)\:\leqslant\:\mathrm{2}{x}^{\mathrm{2}} \:−\:\mathrm{4}{x}\:+\:\mathrm{4} \\ $$$$\mathrm{for}\:\mathrm{every}\:\:{x}\:\in\:\mathbb{R} \\ $$$$\mathrm{If}\:{f}\left(\mathrm{5}\right)\:=\:\mathrm{26},\:\mathrm{then}\:{f}\left(\mathrm{7}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:… \\ $$$$ \\ $$$$\left({A}\right)\:\mathrm{38}\:\:\:\:\:\:\:\:\:\left({D}\right)\:\mathrm{74} \\ $$$$\left({B}\right)\:\mathrm{50}\:\:\:\:\:\:\:\:\:\left({E}\right)\:\mathrm{92} \\…
Question Number 152671 by liberty last updated on 31/Aug/21 Commented by MJS_new last updated on 31/Aug/21 $${f}\left(\mathrm{1}\right)=\mathrm{5} \\ $$$${f}\left(\mathrm{2}\right)={f}\left(\mathrm{1}+\mathrm{1}\right)={f}\left(\mathrm{1}\right)+\mathrm{6}×\mathrm{1}+\mathrm{4}=\mathrm{15} \\ $$$${f}\left(\mathrm{3}\right)={f}\left(\mathrm{2}+\mathrm{1}\right)={f}\left(\mathrm{2}\right)+\mathrm{6}×\mathrm{2}+\mathrm{4}=\mathrm{31} \\ $$$$\mathrm{but} \\ $$$${f}\left(\mathrm{3}\right)={f}\left(\mathrm{3}×\mathrm{1}\right)=\mathrm{4}{f}\left(\mathrm{1}\right)+\mathrm{1}=\mathrm{21}…
Question Number 21491 by dioph last updated on 24/Sep/17 $$\mathrm{If}\:{Y}\:\mathrm{is}\:\mathrm{a}\:\mathrm{non}−\mathrm{void}\:\mathrm{set},\:\mathrm{define}\:{Y}^{{T}} \:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{the}\:\mathrm{collection}\:\mathrm{of}\:\mathrm{all}\:\mathrm{functions}\:\mathrm{with} \\ $$$$\mathrm{domain}\:{T}\:\mathrm{and}\:\mathrm{range}\:{Y}.\:\mathrm{Show}\:\mathrm{that} \\ $$$$\mathrm{if}\:{T}\:\mathrm{and}\:{Y}\:\mathrm{are}\:\mathrm{finite}\:\mathrm{sets}\:\mathrm{with}\:{m}\:\mathrm{and} \\ $$$${n}\:\mathrm{elements},\:\mathrm{then}\:{Y}^{{T}} \:\mathrm{has}\:{n}^{{m}} \:\mathrm{elements}. \\ $$ Terms of…