34.6. Find the function $f(x)$, which is defined for all $x$, is non-zero at some point, and for all $x, y$ satisfies the equation $f(x) f(y)=f(x-y)$.
34.6. Let's take a point $x_{0}$ for which $f\left(x_{0}\right) \neq 0$, and set $y=0$. Then $f\left(x_{0}\right) f(0)=f\left(x_{0}\right)$, so $f(0)=1$. Setting $x=y$, we get $(f(x))^{2}=f(0)=1$. Therefore, $f(x)= \pm 1$. Finally, setting $y=x / 2$, we obtain $f(x) f(x / 2)=f(x / 2)$, and since $f(x / 2)= \pm 1 \neq 0$, it follows that $f(x)=1$.