Bài 1: Cho $f:\mathbb{R}\rightarrow \mathbb{R}$ thỏa mãn $4f\left ( f\left ( x \right ) \right )=2f\left ( x \right )+x$. Chứng minh $f\left ( 0 \right )=0.$
Bài 2: Tìm hàm $f:\mathbb{Q}^{+}\rightarrow \mathbb{Q}^{+}$ thỏa mãn
$i)f\left ( x+1 \right )=f\left ( x \right )+1 \forall x \in \mathbb{Q}^{+}$
$ii)f\left ( x^{2} \right )=\left [ f\left ( x \right ) \right ]^{2}+1 \forall x \in \mathbb{Q}^{+}$