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 \(c:\) \[f(x)=\cases{\begin{align} &x+a &&\text{for }|x|<2\\&bf\Big(\frac{x}{2}\Big)+c &&\text{for }|x|\ge2. \end{align}}\] Find the value of \(\frac{100}{a}+\frac{100}{b}+\frac{100}{c}.\)