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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
 #1
avatar+4490 
+1

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
 #2
avatar+99384 
+1

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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