The full question :
Find 2 functions $f,g: \mathbb R \to \mathbb R$
$f,g \neq 0 $
so that $fg = 0$
The confusing part is the way it is written, as far as I can tell there is no product of anything other than $0$ which yields $0$, is there??
Perhaps they meant $f(g(x))$ in this question?
Thanks in advance