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Category: Algebra

xf-x-g-x-h-x-2x-1-f-x-2x-2-g-x-3h-x-x-ln-x-f-x-x-3-h-x-1-Find-f-x-g-x-h-x-

Question Number 19123 by 433 last updated on 05/Aug/17 $$\begin{cases}{\mathrm{xf}\left(\mathrm{x}\right)−\mathrm{g}\left(\mathrm{x}\right)+\mathrm{h}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{1}}\\{\mathrm{f}\left(\mathrm{x}\right)−\left(\mathrm{2x}−\mathrm{2}\right)\mathrm{g}\left(\mathrm{x}\right)−\mathrm{3h}\left(\mathrm{x}\right)=\mathrm{x}}\\{\mathrm{ln}\:\left(\mathrm{x}\right)\mathrm{f}\left(\mathrm{x}\right)−\left(\mathrm{x}−\mathrm{3}\right)\mathrm{h}\left(\mathrm{x}\right)=\mathrm{1}}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{f}\left(\mathrm{x}\right),\mathrm{g}\left(\mathrm{x}\right),\mathrm{h}\left(\mathrm{x}\right) \\ $$ Answered by ajfour last updated on 05/Aug/17 $$\mathrm{x}\left(\mathrm{2x}−\mathrm{2}\right)\mathrm{f}−\left(\mathrm{2x}−\mathrm{2}\right)\mathrm{g}+\left(\mathrm{2x}−\mathrm{2}\right)\mathrm{h}=\left(\mathrm{2x}−\mathrm{2}\right)\left(\mathrm{2x}+\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{f}−\left(\mathrm{2x}−\mathrm{2}\right)\mathrm{g}−\mathrm{3h}=\mathrm{x} \\…

Question-150199

Question Number 150199 by mathdanisur last updated on 10/Aug/21 Commented by Rasheed.Sindhi last updated on 10/Aug/21 $$\mathrm{Is}\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\pi?\:\mathrm{Are}\:\mathrm{x},\mathrm{y}\:\&\:\mathrm{z}\:\mathrm{the}\:\mathrm{angles} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}? \\ $$ Terms of Service Privacy…

Solve-the-equation-x-3-x-2-x-2-0-

Question Number 150189 by mathdanisur last updated on 10/Aug/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\left(\mathrm{x}\:-\:\mathrm{3}\right)\:\sqrt{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{x}\:−\:\mathrm{2}}\:=\:\mathrm{0} \\ $$ Commented by Skabetix last updated on 10/Aug/21 $${x}=\mathrm{3}\:{or}\:{x}=\mathrm{2}\:{or}\:{x}=−\mathrm{1} \\ $$…

x-y-7-y-x-7-xy-

Question Number 150191 by mathdanisur last updated on 10/Aug/21 $$\begin{cases}{\mathrm{x}\:-\:\sqrt{\mathrm{y}}\:=\:\mathrm{7}}\\{\mathrm{y}\:+\:\sqrt{\mathrm{x}}\:=\:\mathrm{7}}\end{cases}\:\:\:\Rightarrow\:\:\mathrm{xy}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 10/Aug/21 $$\begin{cases}{\mathrm{x}\:-\:\underset{\mathrm{v}} {\underbrace{\sqrt{\mathrm{y}}}}\:=\:\mathrm{7}}\\{\mathrm{y}\:+\:\underset{\mathrm{u}} {\underbrace{\sqrt{\mathrm{x}}}}\:=\:\mathrm{7}}\end{cases}\:\:\:\Rightarrow\:\:\mathrm{xy}\:=\:? \\ $$$$\mathrm{u}^{\mathrm{2}} −\mathrm{v}=\mathrm{7}\:\wedge\:\mathrm{v}^{\mathrm{2}}…

If-f-x-2x-2-5-f-1-2-

Question Number 150187 by mathdanisur last updated on 10/Aug/21 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{5}\:\:\Rightarrow\:\:\mathrm{f}^{\:−\mathrm{1}} \left(\mathrm{2}\right)\:=\:? \\ $$ Commented by amin96 last updated on 10/Aug/21 $$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}=\mathrm{2}\:\:\Rightarrow\:\:\:{x}=\pm\frac{\mathrm{3}{i}}{\:\sqrt{\mathrm{2}}}\:\:\: \\ $$$${f}\left(\pm\frac{\mathrm{3}{i}}{\:\sqrt{\mathrm{2}}}\right)=\mathrm{2}\:\:\:\:\Rightarrow\:\:{f}^{−\mathrm{1}}…

x-6-3-x-5-3-x-4-3-3-x-6-x-5-x-4-x-

Question Number 150181 by liberty last updated on 10/Aug/21 $$\:\left(\mathrm{x}−\mathrm{6}\right)^{\mathrm{3}} +\left(\mathrm{x}−\mathrm{5}\right)^{\mathrm{3}} +\left(\mathrm{x}−\mathrm{4}\right)^{\mathrm{3}} =\mathrm{3}\left(\mathrm{x}−\mathrm{6}\right)\left(\mathrm{x}−\mathrm{5}\right)\left(\mathrm{x}−\mathrm{4}\right) \\ $$$$\mathrm{x}=? \\ $$ Answered by Rasheed.Sindhi last updated on 13/Aug/21 $$\:\left(\mathrm{x}−\mathrm{6}\right)^{\mathrm{3}}…

If-f-x-sin-4-3x-f-pi-12-

Question Number 150186 by mathdanisur last updated on 10/Aug/21 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{sin}^{\mathrm{4}} \left(\mathrm{3x}\right)\:\:\Rightarrow\:\:{f}\:^{'} \left(\frac{\pi}{\mathrm{12}}\right)\:=\:? \\ $$ Answered by puissant last updated on 10/Aug/21 $$\mathrm{f}'\left(\mathrm{x}\right)=\mathrm{4}×\mathrm{3cos}\left(\mathrm{3x}\right)\mathrm{sin}^{\mathrm{3}} \left(\mathrm{3x}\right) \\ $$$$\Rightarrow\:\mathrm{f}'\left(\mathrm{x}\right)=\mathrm{12cos}\left(\mathrm{3x}\right)\mathrm{sin}^{\mathrm{3}}…

A-polynomial-f-x-with-rational-coefficients-leaves-remainder-15-when-divided-by-x-3-and-remainder-2x-1-when-divided-by-x-1-2-Find-the-remainder-when-f-x-is-divided-by-x-3-x-1-2-

Question Number 19101 by Tinkutara last updated on 04/Aug/17 $$\mathrm{A}\:\mathrm{polynomial}\:{f}\left({x}\right)\:\mathrm{with}\:\mathrm{rational} \\ $$$$\mathrm{coefficients}\:\mathrm{leaves}\:\mathrm{remainder}\:\mathrm{15},\:\mathrm{when} \\ $$$$\mathrm{divided}\:\mathrm{by}\:{x}\:−\:\mathrm{3}\:\mathrm{and}\:\mathrm{remainder}\:\mathrm{2}{x}\:+\:\mathrm{1}, \\ $$$$\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\left({x}\:−\:\mathrm{1}\right)^{\mathrm{2}} .\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{remainder}\:\mathrm{when}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by} \\ $$$$\left({x}\:−\:\mathrm{3}\right)\left({x}\:−\:\mathrm{1}\right)^{\mathrm{2}} . \\ $$ Commented…