Question Number 211402 by efronzo1 last updated on 08/Sep/24
Answered by A5T last updated on 08/Sep/24
$${Q}\mathrm{211029},\:{we}\:{can}\:{find}\:{a}\:{polynomial}\:{f}\left({x}\right) \\ $$$${f}\left({x}\right)={x}^{{n}} \underset{−} {+}\mathrm{1} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{28}\Rightarrow{f}\left({x}\right)={x}^{\mathrm{3}} +\mathrm{1} \\ $$$$\left({x}^{\mathrm{3}} +\mathrm{1}\right)\left(\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+\mathrm{1}\right)=\left({x}^{\mathrm{3}} +\mathrm{1}\right)+\left(\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+\mathrm{1}\right) \\ $$$$\Rightarrow{f}\left(−\mathrm{2}\right)+{f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)=−\left(\mathrm{6}\frac{\mathrm{1}}{\mathrm{8}}\right)=−\frac{\mathrm{49}}{\mathrm{8}} \\ $$