Let \( f:[0,1]\to\mathbb{R} \) and \( g:[0,1]\to\mathbb{R} \) be defined as:
\[
f(x)=
\begin{cases}
1, & x \text{ rational}\\
0, & x \text{ irrational}
\end{cases}
\quad
g(x)=
\begin{cases}
0, & x \text{ rational}\\
1, & x \text{ irrational}
\end{cases}
\]
Then: