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Let f(x) be a function which contains 2 in its domain and range. Suppose that f(f(x))*(1+(f(x)) = -f(x) for all numbers x in the domain of f(x).


Thank you for your help.

 Oct 16, 2018

I did two of these for you... from what class are you getting these questions?


I was able to see the trick in the first two but this one seems truly complicated.


Is your class teaching any strategies for dealing with these?

 Oct 18, 2018

How about this.


\(f(f(x))*(1+(f(x)) = -f(x)\\ so\\ f(f(2))*(1+(f(2)) = -f(2)\\ let\;\;\; f(2)=k\\ f(k)*(1+k) = -k\\ f(k)= \frac{-k}{1+k}\\ \)


This has to work for all the other values in the domain as well so I will replace k with x


\(f(x)= \frac{-x}{1+x}\\\)



This contains 2 in its range as well as its domain.


 Oct 18, 2018

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