# algebra

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Given f(11)=11 and f(x+3) = (f(x)-1)/(f(x)+1) for all x, find f(2000)

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Turfe

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Hey, thank me in class for doing your work for you :P

Look for the pattern
f(11) = 11
f(14) = (11 - 1)/(11 + 1) = 10/12 = 5/6
f(17) = (5/6 - 1)/(5/6 + 1) = (-1/6) / (11/6) = -1/11
f(20) = (-1/11 - 1)/(-1/11 + 1) = -12/11 / (10/11) = -12/10 = -6/5
f(23) = (-6/5 - 1)/(-6/5 + 1) = -11/5 / (-1/5) = 11

so it repeats every 12 numbers (23 - 11 = 12)

and since 2000 = 165 • 12 + 20, f(2000) will be the same as f(20) = -6/5

:P

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