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Question Number 190618 by mustafazaheen last updated on 07/Apr/23

f(x−f(x))=x  ,f(5)=−1  f(−1)=?

$$\mathrm{f}\left(\mathrm{x}−\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{x}\:\:,\mathrm{f}\left(\mathrm{5}\right)=−\mathrm{1} \\ $$$$\mathrm{f}\left(−\mathrm{1}\right)=? \\ $$

Answered by aba last updated on 07/Apr/23

f(5−f(5))=5⇒ f(4)=5  f(4−f(4))=4⇒f(−1)=4

$$\mathrm{f}\left(\mathrm{5}−\mathrm{f}\left(\mathrm{5}\right)\right)=\mathrm{5}\Rightarrow\:\mathrm{f}\left(\mathrm{4}\right)=\mathrm{5} \\ $$$$\mathrm{f}\left(\mathrm{4}−\mathrm{f}\left(\mathrm{4}\right)\right)=\mathrm{4}\Rightarrow\mathrm{f}\left(−\mathrm{1}\right)=\mathrm{4} \\ $$$$\:\:\:\:\: \\ $$

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