Let $f$ be a continuous function on $[0,4]$. If $f(x)$ takes rational values for all $x$ and $f(4)=2

Question

Let $f$ be a continuous function on $[0,4]$. If $f(x)$ takes rational values for all $x$ and $f(4)=2025$, then $f(\pi)$ is

Professor PC Thomas Classes · Answer

Continuous function taking only rational values must be constant. $f(\pi)=2025$.