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A continuous function f(x)f(x)f(x) is defined as follows for some non-zero constants a,a,a, b,b,b, and c:c:c: f(x)={x+afor ∣x∣<2bf(x2)+cfor ∣x∣≥2.f(x)=\cases{\begin{aligned} &x+a &&\text{for }|x|<2\\&bf\Big(\frac{x}{2}\Big)+c &&\text{for }|x|\ge2. \end{aligned}}f(x)=⎩⎨⎧x+abf(2x)+cfor ∣x∣<2for ∣x∣≥2. Find the value of 100a+100b+100c.\frac{100}{a}+\frac{100}{b}+\frac{100}{c}.a100+b100+c100.
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