Figure-It-Out Function! - Part 4: Semi G.P.

Let there be a function $f:\mathbb{Z}\rightarrow\mathbb{R}$ , such that

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

$f(1)=2$

$f(2)=1$

Find $f(2016)$

There is an odd property exhibited in this question and FIOF 2 . Can you find it, and prove why it is so?

This problem is part of the Figure-It-Out Function! series.