7. $\left[-1,-\frac{1}{2}\right) \cup(0,1]$ From the graph, we know that $f(x)$ is an odd function, hence $f(x)-f(-x)=2 f(x)>-1$, so $f(x)>-\frac{1}{2}$. From the graph, we know that $-1 \leqslant x \leqslant-\frac{1}{2}, 0<x \leqslant 1$. Therefore, the answer is $\left[-1,-\frac{1}{2}\right) \cup(0,1]$.
7. The graph of $f(x)$ consists of two line segments (missing one endpoint), its domain is $[-1,0) \cup(0,1]$, then the solution set of the inequality $f(x)-f(-x)>-1$ is