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Category: Relation and Functions

f-x-y-2-f-x-y-2-g-x-g-x-y-g-x-y-f-x-2-f-y-2-f-x-g-x-

Question Number 57011 by 121194 last updated on 28/Mar/19 $${f}\left(\frac{{x}+{y}}{\mathrm{2}}\right){f}\left(\frac{{x}−{y}}{\mathrm{2}}\right)={g}\left({x}\right) \\ $$$${g}\left({x}+{y}\right){g}\left({x}−{y}\right)=\left[{f}\left({x}\right)\right]^{\mathrm{2}} −\left[{f}\left({y}\right)\right]^{\mathrm{2}} \\ $$$${f}\left({x}\right),{g}\left({x}\right)=? \\ $$ Answered by kaivan.ahmadi last updated on 28/Mar/19 $${g}\left({x}\right)…

find-function-f-x-and-g-x-such-that-f-2x-1-g-1-x-x-1-f-x-x-1-2g-1-2x-2-3-

Question Number 187988 by cortano12 last updated on 24/Feb/23 $$\:\mathrm{find}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right) \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\begin{cases}{\mathrm{f}\left(\mathrm{2x}−\mathrm{1}\right)+\mathrm{g}\left(\mathrm{1}−\mathrm{x}\right)=\mathrm{x}+\mathrm{1}}\\{\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}+\mathrm{1}}\right)+\mathrm{2g}\left(\frac{\mathrm{1}}{\mathrm{2x}+\mathrm{2}}\right)=\mathrm{3}}\end{cases} \\ $$ Answered by MathGuy last updated on 24/Feb/23 $${Answer}\::−\:{do}\:{x}\rightarrow{x}+\mathrm{1}\:{in}\:{eq}.\mathrm{1}\:\&\:{x}\rightarrow{x}−\mathrm{1}\:{in}\:{eq}.\mathrm{2} \\ $$$${you}\:{will}\:{get} \\…

Find-the-solution-of-recurrence-relation-a-n-2a-n-1-3a-n-2-with-a-0-1-a-1-2-

Question Number 56864 by Joel578 last updated on 25/Mar/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{recurrence}\:\mathrm{relation} \\ $$$${a}_{{n}} \:=\:\mathrm{2}{a}_{{n}−\mathrm{1}} \:+\:\mathrm{3}{a}_{{n}−\mathrm{2}} ,\:\mathrm{with}\:{a}_{\mathrm{0}} \:=\:\mathrm{1},\:{a}_{\mathrm{1}} \:=\:\mathrm{2} \\ $$ Commented by maxmathsup by imad last…

let-Z-n-x-sin-narcsinx-with-n-integr-1-determine-roots-of-Z-n-x-2-decompose-the-fraction-F-1-Z-n-x-

Question Number 56832 by maxmathsup by imad last updated on 24/Mar/19 $${let}\:\:{Z}_{{n}} \left({x}\right)={sin}\left({narcsinx}\right)\:\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{roots}\:{of}\:{Z}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{the}\:{fraction}\:{F}\:=\frac{\mathrm{1}}{{Z}_{{n}} \left({x}\right)} \\ $$ Terms of Service Privacy…

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Question Number 56831 by maxmathsup by imad last updated on 24/Mar/19 $${let}\:{f}\left({x}\right)\:=\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}−\mathrm{2}{x}\:−\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx} \\ $$$$\left.\mathrm{2}\right){determine}\:{f}^{−\mathrm{1}} \left({x}\right)\:{and}\:{calculate}\:\int\:{f}^{−\mathrm{1}} \left({x}\right){dx}\:. \\ $$ Commented by…