Question Number 145000 by imjagoll last updated on 01/Jul/21
$$\mathrm{If}\:\mathrm{F}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{F}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{x}^{\mathrm{2}} \\ $$$$\mathrm{then}\:\mathrm{F}^{−\mathrm{1}} \left(\mathrm{x}\right)=? \\ $$
Commented by prakash jain last updated on 01/Jul/21
$${f}\left({x}+\mathrm{1}\right)={x}^{\mathrm{2}} \Rightarrow{f}\left({x}\right)=\left({x}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$${f}\left({x}−\mathrm{1}\right)={x}^{\mathrm{2}} \Rightarrow{f}\left({x}\right)=\left({x}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\mathrm{Please}\:\mathrm{recheck}\:\mathrm{question}. \\ $$$${f}\left({x}\right)\:\mathrm{is}\:\mathrm{periodic}? \\ $$