7. Let $f(x)$ be a function such that $f(1)=1, f(2)=2$ and $f(x+2)=f(x+1)-f(x)$. Find $f(2016)$.
Answer: -1
Solution:
$$
\begin{aligned}
f(1)= & 1 \\
f(2)= & 2 \\
f(3)= & f(2)-f(1)=2-1=1 \\
f(4)= & f(3)-f(2)=1-2=-1 \\
f(5)= & f(4)-f(3)=-1-1=-2 \\
f(6)= & f(5)-f(4)=-2-(-1)=-1 \\
f(7)= & f(6)-f(5)=-1-(-2)=1 \\
f(8)= & f(7)-f(6)=1-(-1)=2 \\
& \vdots
\end{aligned}
$$

Observe that this pattern will repeat itself every six, and thus, $f(2016)=f(6)=-1$.