7. The function
$$
f(x)=\frac{\sin x-1}{\sqrt{3-2 \cos x-2 \sin x}}(0 \leqslant x \leqslant 2 \pi)
$$

has the range . $\qquad$
7. $[-1,0]$.

Let $1-\sin x=a, 1-\cos x=b$. Then
$$
y=f(x)=\frac{-a}{\sqrt{a^{2}+b^{2}}}(0 \leqslant a \leqslant 1,0 \leqslant b \leqslant 1),
$$

and the point $P(a, b)$ lies on the circle $(x-1)^{2}+(y-1)^{2}=1$. Let the inclination angle of the line $O P$ be $\theta$. Then
$$
0 \leqslant \theta \leqslant \frac{\pi}{2} \text {. }
$$

Therefore, $y=-\cos \theta \in[-1,0]$.