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Australian AMC 2014 - Senior Question 20

AMC AUSTRALIA · Australian AMC 2014 - Senior

Question 20

Given $f_1(x)=x/(x+1)$ and $f_{n+1}(x)=f_1(f_n(x))$, what is $f_{2014}(x)$?
  1. $x/(2014x+1)$
  2. $2014x/(2014x+1)$
  3. $x/(x+2014)$
  4. $2014x/(x+1)$
  5. $x/(2014(x+1))$