Period

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November 5th 2009, 07:10 AM
dhiab

Period : 1

Find the period for the function f in R:
$f(x+1)=\frac{1}{1-f(x)}$
November 5th 2009, 07:18 AM
red_dog

$f(x+2)=\frac{1}{1-f(x+1)}=\frac{1}{1-\displaystyle\frac{1}{1-f(x)}}=\frac{f(x)-1}{f(x)}=1-\frac{1}{f(x)}$

$f(x+3)=1-\frac{1}{f(x+1)}=1-1+f(x)=f(x)$

Then the period is 3.

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