Math Help - Period

1. Period : 1

Find the period for the function f in R:
$f(x+1)=\frac{1}{1-f(x)}$

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

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

Then the period is 3.