The set of all real values of $x$ for which $f(x)=\sqrt{\frac{|x|-2}{|x|-3}}$ is a well defined function is

$f(x)$ is a quadratic polynomial satisfying the condition $f(x)+f\left(\frac{1}{x}\right)=f(x) f\left(\frac{1}{x}\right)$. If $f(-1)=0$, then the range of $f$ is

$$ \sum\limits_{k=1}^n k(k+1)(k+2) \ldots(k+r-1)= $$

If $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6\end{array}\right]$ and $|\operatorname{adj}(\operatorname{adj} A)|(\operatorname{adj} A)^{-1}=k A$, then $k=$