TIFR Mathematics 2024 | Part B | Question: 14

Question

There exists a unique function $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f$ is continuous at $x=0$, and such that for all $x \in \mathbb{R}$
\[
f(x)+f\left(\frac{x}{2}\right)=x .
\]