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.

thess
Oct 16, 2018

#1**+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?

Rom
Oct 18, 2018

#2**+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.

Melody
Oct 18, 2018