If $f(x)$ is defined nowhere, and $z(x)$ is zero everywhere, then what is $f(x)z(x)$?

Question

Let $f(x)=\mu y(id^2_1(x+1,y)=0)$ and $g(x)=f(x)z(x)$ where $id^2_1(x,y)=x$ and $z(x)=0$. Then $f(x)$ is defined nowhere and $z(x)=0$ everywhere. Then what is the value of $g$? Is it undefined or just zero?