Question 16
Find all functions $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, for which:
$$
f(xf(x,z), yf(y,z)) = f(x,z)f(y,z)
$$
for every real numbers $x$, $y$ and $z$ and $f(0,0) \neq 0$.
$$
f(xf(x,z), yf(y,z)) = f(x,z)f(y,z)
$$
for every real numbers $x$, $y$ and $z$ and $f(0,0) \neq 0$.