Question 182
Find all functions $f(x): \mathbb{R} \to \mathbb{R}$ satisfying the equality
$$
x = -\frac{1}{2}f(|x|) + |f(x)|
$$
for all real numbers $x$.
$$
x = -\frac{1}{2}f(|x|) + |f(x)|
$$
for all real numbers $x$.
MathNet 2019-part-01 — 184 problems (EN–VI) Question 182
Math Olympiad Vault · MathNet 2019-part-01 — 184 problems (EN–VI)