Question Number 151859 by puissant last updated on 23/Aug/21 Commented by OlafThorendsen last updated on 23/Aug/21 $$\left.\mathrm{1}\right) \\ $$$${U}_{{n}} \:=\:\int_{\mathrm{0}} ^{\pi} \mathrm{sin}^{\mathrm{2}{n}} {t}\:{dt} \\ $$$${U}_{\mathrm{0}}…
Question Number 151742 by mnjuly1970 last updated on 22/Aug/21 $$\:\: \\ $$$$\:\:\:\mathrm{F}\:\left({x}\:\right):=\:\frac{{log}\:\left({sin}\left({x}\right)\:+{cos}\:\left({x}\right)\right)}{{log}\:\left({sin}\left(\mathrm{2}{x}\right)\right)} \\ $$$$\:\:{find}\:\:\:{the}\:{Domain}\:{of}\:\:\:\:\mathrm{F}\:… \\ $$$$\:\:\:\mathrm{D}_{\:\mathrm{F}} \:=? \\ $$ Answered by mindispower last updated on…
Question Number 86189 by oustmuchiya@gmail.com last updated on 27/Mar/20 $${Given}\:{that}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{7}}{\mathrm{8}}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\:\frac{\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{6}}{\mathrm{6}},\:{find} \\ $$$$\left(\mathrm{a}\right)\:\boldsymbol{\mathrm{g}}\left(\mathrm{6}\right),\:\left(\mathrm{b}\right)\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\mathrm{c}\right)\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{\mathrm{x}}\:{if}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right) \\ $$ Answered by Kunal12588 last updated on 27/Mar/20 $$\left({a}\right)\:{g}\left(\mathrm{6}\right)=\frac{\mathrm{18}−\mathrm{6}}{\mathrm{6}}=\mathrm{2} \\ $$$$\left({b}\right)\:{f}^{−\mathrm{1}}…
Question Number 86160 by jagoll last updated on 27/Mar/20 $$\mathrm{If}\:\left(\mathrm{x}−\mathrm{1}\right)\:\mathrm{f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}} \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right)\: \\ $$ Commented by john santu last updated on 27/Mar/20 $${replace}\:{x}\:{by}\:\frac{\mathrm{1}}{{x}} \\ $$$$\Rightarrow\left(\frac{\mathrm{1}}{{x}}−\mathrm{1}\right){f}\left(\frac{\mathrm{1}}{{x}}\right)+{f}\left({x}\right)=\:\frac{\mathrm{1}}{\frac{\mathrm{1}}{{x}}−\mathrm{1}}…
Question Number 86129 by oustmuchiya@gmail.com last updated on 27/Mar/20 $${Given}\:{that}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{8}\boldsymbol{\mathrm{x}}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{2}}{\mathrm{4}},\:{find} \\ $$$$\left(\mathrm{a}\right)\:\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\mathrm{b}\right)\:{an}\:{expression}\:{for}\:\boldsymbol{{fg}}\left(\boldsymbol{\mathrm{x}}\right) \\ $$$$\left(\mathrm{c}\right)\:{value}\:{of}\:\boldsymbol{\mathrm{x}}\:{which}\:\boldsymbol{\mathrm{fg}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{20}\: \\ $$ Commented by jagoll last updated on 27/Mar/20 $$\left.\mathrm{a}\right)\:\mathrm{f}^{−\mathrm{1}}…
Question Number 86030 by oustmuchiya@gmail.com last updated on 26/Mar/20 $${Tbe}\:{function}\:\boldsymbol{\mathrm{f}}\:{and}\:\boldsymbol{\mathrm{g}}\:{are}\:{defined}\:{by}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{3}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{3}\boldsymbol{\mathrm{x}}. \\ $$$$\boldsymbol{\mathrm{F}}{ind}\:\left(\boldsymbol{\mathrm{a}}\right)\:\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\:\left(\boldsymbol{\mathrm{b}}\right)\:\boldsymbol{\mathrm{gf}}\left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\boldsymbol{\mathrm{c}}\right)\:\boldsymbol{\mathrm{gf}}\left(\mathrm{2}\right) \\ $$ Commented by Rio Michael last updated on 26/Mar/20 $$\:{f}:\:{x}\:\rightarrow\:\mathrm{2}{x}−\mathrm{3}\:\:\:\mathrm{and}\:\mathrm{g}\::\:{x}\:\rightarrow\:\mathrm{3}{x} \\…
Question Number 20279 by ajfour last updated on 25/Aug/17 $${Determine}\:{a}\:{relation}\:{between}\:\:{the} \\ $$$${coefficients}\:\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}},\:\boldsymbol{{d}}\:{such}\:{that}\:{the} \\ $$$${equation}:\:\:{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${has}\:{three}\:{real}\:{roots}\:\left({with}\:{a}\:{pair}\right. \\ $$$$\left.{of}\:{double}\:{roots}\right). \\ $$ Terms of Service…
Question Number 151208 by liberty last updated on 19/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 19982 by Tinkutara last updated on 19/Aug/17 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ordered}\:\mathrm{pairs} \\ $$$$\left({A},\:{B}\right)\:\mathrm{where}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{subsets}\:\mathrm{of} \\ $$$$\left\{\mathrm{1},\:\mathrm{2},\:…,\:\mathrm{5}\right\}\:\mathrm{such}\:\mathrm{that}\:\mathrm{neither}\:{A}\:\subseteq\:{B} \\ $$$$\mathrm{nor}\:{B}\:\subseteq\:{A}? \\ $$ Commented by mrW1 last updated on 22/Aug/17…
Question Number 19978 by Tinkutara last updated on 19/Aug/17 $$\mathrm{Let}\:{f}\:\mathrm{be}\:\mathrm{a}\:\mathrm{one}-\mathrm{to}-\mathrm{one}\:\mathrm{function}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{to}\:\mathrm{itself} \\ $$$$\mathrm{such}\:\mathrm{that}\:{f}\left({mn}\right)\:=\:{f}\left({m}\right){f}\left({n}\right)\:\mathrm{for}\:\mathrm{all} \\ $$$$\mathrm{natural}\:\mathrm{numbers}\:{m}\:\mathrm{and}\:{n}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{least}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{f}\left(\mathrm{999}\right)? \\ $$ Answered by mrW1 last updated…