1. The range of the function $f(x)=x^{2}-x^{2} \sqrt{1-x^{2}}$ is
-, 1. $[0,1]$.
Note that, $f(x)=x^{2}\left(1-\sqrt{1-x^{2}}\right)$.
Obviously, the domain of $f(x)$ is $[-1,1]$, and $f(x)$ is an even function.

When $x \in[0,1]$, $x^{2}$ and $1-\sqrt{1-x^{2}}$ are both increasing functions, thus, $f(x)$ is an increasing function, the range of $f(x)$ is $[f(0), f(1)]$, i.e., $[0,1]$.