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

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