Christmas Streak 41/88: Func(ep)tion

Calculus Level 3

A continuous function $f(x)$ is defined as follows for some non-zero constants $a,$ $b,$ and $c:$ $f(x)=\cases{\begin{aligned} &x+a &&\text{for }|x|<2\\&bf\Big(\frac{x}{2}\Big)+c &&\text{for }|x|\ge2. \end{aligned}}$ Find the value of $\frac{100}{a}+\frac{100}{b}+\frac{100}{c}.$