+0  
 
0
85
1
avatar

Define f(x) = (1 + x)/(1 - x) and g(x) = 1/x. Find the value of g(f(g(f(... g(f(12)) ... )))) where there are 16 compositions of the functions g, and f, alternating between the two.

 Dec 24, 2020
 #1
avatar+117724 
+1

Let's see if  we  have some sort of repeating pattern here

 

First composition

f(12)  = 13/11

g (f(12)) = g ( 13/11) = 11/13

 

Second composition

f(11/13)  =  12

g (12)  = 1/12

 

Third composition

f(1/12)  =  13/11

g(13/11)  =   11/13

 

The pattern repeats afer 2 compositions  .......so ater 16 compositions we will end up with  1/12

 

 

cool cool cool

 Dec 24, 2020

9 Online Users

avatar
avatar