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Question Number 218256 by mr W last updated on 03/Apr/25
Answered by efronzo1 last updated on 03/Apr/25
$$\:\:\mathrm{f}\left(\mathrm{3}\right)+\mathrm{f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)=\:\mathrm{72} \\ $$$$\:\mathrm{f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)+\:\mathrm{f}\left(\frac{\mathrm{2}}{\mathrm{3}}\right)=−\mathrm{12} \\ $$$$\:\mathrm{f}\left(\frac{\mathrm{2}}{\mathrm{3}}\right)+\:\mathrm{f}\left(\mathrm{3}\right)\:=\:\mathrm{16} \\ $$$$\:\:\mathrm{2}\left\{\mathrm{f}\left(\mathrm{3}\right)+\:\mathrm{f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)+\:\mathrm{f}\left(\frac{\mathrm{2}}{\mathrm{3}}\right)\right\}\:=\:\mathrm{76} \\ $$$$\:\:\mathrm{f}\left(\mathrm{3}\right)+\:\left(−\mathrm{12}\right)\:=\:\mathrm{38} \\ $$$$\:\:\mathrm{f}\left(\mathrm{3}\right)\:=\:\mathrm{50} \\ $$
Commented by mr W last updated on 04/Apr/25
$${thanks}! \\ $$
Answered by mahdipoor last updated on 03/Apr/25
$${f}\left({x}\right)+{f}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)=\mathrm{24}{x} \\ $$$${f}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)+{f}\left(\frac{\mathrm{1}−{x}}{−{x}}\right)=\frac{\mathrm{24}}{\mathrm{1}−{x}} \\ $$$${f}\left(\frac{\mathrm{1}−{x}}{−{x}}\right)+{f}\left({x}\right)=\frac{\mathrm{24}\left(\mathrm{1}−{x}\right)}{−{x}} \\ $$$$\Rightarrow\Rightarrow{f}\left({x}\right)=\mathrm{12}\left({x}+\frac{\mathrm{1}}{\mathrm{1}−{x}}−\frac{\mathrm{1}−{x}}{{x}}\right) \\ $$
Commented by mr W last updated on 04/Apr/25
$${thanks}! \\ $$