Adding Up a Reflected Function

★ 5/10functions Logarithms Functional Equations

Problem

A function $f(x)$ defined on all of $\mathbb{R}$ satisfies $f(x) = 2^x - x$ for $x \in [0, 1)$ , and

f(x) + f(x+1) = 1 \quad \text{for every real } x.

Let $a = \log_2 3$ . Find the value of $f(a) + f(2a) + f(3a)$ .

Answer

Solution

Difficulty	5/10
Topics	functions, Logarithms, Functional Equations

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