7. The range of the function $f(x)=\frac{\sin x-1}{\sqrt{3-2 \cos x-2 \sin x}}(0 \leqslant x \leqslant 2 \pi)$ is
When $x \neq \frac{\pi}{2}$, $f(x)=\frac{\sin x-1}{\sqrt{(\sin x-1)^{2}+(\cos x-1)^{2}}}=-\frac{1}{\sqrt{1+\left(\frac{\cos x-1}{\sin x-1}\right)^{2}}}$,
Since $k=\frac{\cos x-1}{\sin x-1}$ represents the slope of the line connecting a point on the unit circle $x^{2}+y^{2}=1$ to (1,1), i.e., $k \in[0,+\infty) \Rightarrow f(x) \in[-1,0)$; when $x=\frac{\pi}{2}$, $f(x)=0$.
Therefore, the range of the function $f(x)=\frac{\sin x-1}{\sqrt{3-2 \cos x-2 \sin x}}(0 \leqslant x \leqslant 2 \pi)$ is $[-1,0]$.