Let $f,g$ be continuous on $\mathbb{R}→\mathbb{R}$ and $f(r)=g(r)$ if $r∈\mathbb{Q}$, is it true that $f(x)=g(x)$ for all $x∈\mathbb{R}$
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$