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Define \(f(x)=\frac{1+x}{1-x}\) and \(g(x)=\frac{-2}{x+1}\). Find the value of \(g(f(g(f(\dotsb g(f(12)) \dotsb ))))\) where the function f is applied 8 times, and the function g is applied 8 times, alternating between the two.

 May 29, 2021

Best Answer 

 #1
avatar+2266 
+1

f(12) = -13/11

g(-13/11) = 22

f(22) = -23/21

g(23/21) = 21. 

 

So it looks like each round it subtracts 1. 23 - 8 = 15

 

=^._.^=

 May 29, 2021
 #1
avatar+2266 
+1
Best Answer

f(12) = -13/11

g(-13/11) = 22

f(22) = -23/21

g(23/21) = 21. 

 

So it looks like each round it subtracts 1. 23 - 8 = 15

 

=^._.^=

catmg May 29, 2021

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