Answer
See graph (red).
domain $(-\infty,0)\cup(0,\infty)$, range $(-\infty,0)\cup(0,\infty)$.
Work Step by Step
Step 1. To obtain the graph of $h(x)=\frac{1}{2}(\frac{1}{x})$ from $y=\frac{1}{x}$, compress the curve vertically by a factor of $\frac{1}{2}$. See graph (red).
Step 2. We can find the domain $(-\infty,0)\cup(0,\infty)$ and the range $(-\infty,0)\cup(0,\infty)$.