MathNet 2014 Question 69

Let $f(x) = ax + b$ where $a$ and $b$ are integers. If $f(f(0)) = 0$ and $f(f(f(4))) = 9$, find the value of $f(f(f(f(1)))) + f(f(f(f(2)))) + \cdots + f(f(f(f(2014))))$.