Baire functions are constant?

Baire functions are constant?

Is it true that every Baire function $f:\mathbb{R}\to \mathbb{N}$ must be
constant.
$f:X \to Y$ is a Baire function for $X,Y$ metrizable spaces if $f$ is a
member of $F(X,Y)$, where $F$ is the smallest class of function from $X$
to $Y$ containing continuous functions and being closed under pointwise
limits.