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Let f(x) = (x - 1)/(x + 1).  Compute f(f(f(5))).

 Jun 29, 2020
 #1
avatar+26578 
+1

Put x = 5   into the equation and compute    5-1  / 5+1   = 4/6     this is  f(5)

   now put   4/6 in the equation and compute    this will be  f f(5)

     finally take the last answer you derived and put it in for x in the equation   this will be   f f f(5)

 Jun 29, 2020
 #2
avatar+8340 
+1

\(f(x) = 1 - \dfrac 2{x + 1}\\ f(f(x)) = 1 - \dfrac2{1 - \dfrac2{x + 1} + 1} = 1 - \dfrac1{\dfrac x{x + 1}} = -\dfrac1x\\ f(f(f(x))) = -\dfrac1{\dfrac{x - 1}{x + 1}} = \dfrac{1 + x}{1 - x}\)

 

Now substitute x = 5.

 Jun 29, 2020

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