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). What is the value of f(2)?

thess Oct 24, 2018

#1**+3 **

"*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). What is the value of f(2)?*"

\(f(f(x))*(1+f(x))=-f(x)\\f(f(x))=\frac{-f(x)}{1+f(x)}\\\text{Let }y=f(x)\\f(y)=\frac{-y}{1+y}\\f(2)=\frac{-2}{1+2}\rightarrow -\frac{2}{3}\)

.Alan Oct 24, 2018

#1**+3 **

Best Answer

"*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). What is the value of f(2)?*"

\(f(f(x))*(1+f(x))=-f(x)\\f(f(x))=\frac{-f(x)}{1+f(x)}\\\text{Let }y=f(x)\\f(y)=\frac{-y}{1+y}\\f(2)=\frac{-2}{1+2}\rightarrow -\frac{2}{3}\)

Alan Oct 24, 2018