Question 61
Define $f: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ by $f(x, y) = (2x - y, x + 2y)$. Let $f^0(x, y) = (x, y)$ and, for each $n \in \mathbb{N}$, $f^n(x, y) = f\left(f^{n-1}(x, y)\right)$. Determine the distance between $f^{2016}\left(\frac{4}{5}, \frac{3}{5}\right)$ and the origin.