# 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 $$\frac{100}{a}+\frac{100}{b}+\frac{100}{c}.$$

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