1. Let the function $f(x)=x^{2}(x \in D, D$ be the domain) have the range $\left\{1^{2}, 2^{2}, \cdots, 2012^{2}\right\}$. Then the number of functions $f(x)$ that satisfy this condition is $\qquad$ .
$-、 1.3^{2012}$.
Since 1 is in the range of $f(x)=x^{2}(x \in D)$, therefore, $1 \in D$, or $-1 \in D$, or $-1 、 1 \in D$, there are three possibilities,

Similarly, for any number $k(k=2,3, \cdots, 2012)$, there are also three possibilities.

Therefore, $D$ has $3^{2012}$ possibilities, which means the number of functions $f(x)$ that satisfy the condition is $3^{2012}$.