Question 18
Let $f$ be the function such that
$$
f(x)= \begin{cases}2x & \text{ if } x \leq \frac{1}{2} \\ 2-2x & \text{ if } x \gt \frac{1}{2}\end{cases}
$$
What is the total length of the graph of $\underbrace{f(f(\ldots f}_{2012\ f\text{'s}}(x) \ldots))$ from $x=0$ to $x=1$?
$$
f(x)= \begin{cases}2x & \text{ if } x \leq \frac{1}{2} \\ 2-2x & \text{ if } x \gt \frac{1}{2}\end{cases}
$$
What is the total length of the graph of $\underbrace{f(f(\ldots f}_{2012\ f\text{'s}}(x) \ldots))$ from $x=0$ to $x=1$?