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

 Oct 24, 2018

Best Answer 

 #1
avatar+27847 
+2

"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)?"

 

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

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 Oct 24, 2018
 #1
avatar+27847 
+2
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
 #2
avatar+75 
0

thank you

 Oct 25, 2018
 #3
avatar+75 
0

Hi, can you teach me the computation how you arrive in -2/3? Thank you.

 Oct 25, 2018

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