1. Given the function $f(x)=x^{2}-1$ with domain $D$, and the range is $\{-1,0,1,3\}$. Determine the maximum number of such sets $D$.

Translate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.
2, 1.27.
Since $f(0)=-1, f( \pm 1)=0$,
$$
f( \pm \sqrt{2})=1, f( \pm 2)=3 \text {, }
$$

Therefore, $0 \in D$; at least one from each of the sets $\{-1,1\}$, $\{-\sqrt{2}, \sqrt{2}\}$, and $\{-2,2\}$ belongs to $D$.
Thus, there are $3 \times 3 \times 3=27$ such $D$'s.