Answer
$\left.\begin{array}{ccc}
& domain & range\\
\hline f(x) & (-\infty,\infty) & (0,\infty)\\
g(x) & (0,\infty) & (-\infty,\infty)
\end{array}\right.$
Work Step by Step
$ f(x)=a^{x}$ and $ g(x)=\log_{a}x $ are inverse functions.
Graphs of inverse functions are reflections of each other, over the line $ y=x.$
The graph of $(\displaystyle \frac{1}{3})^{x}$ is always above the x-axis, falls from the far left rapidly, passes through $(-3,27),(-2,9),(-1,3)$, intersects the y-axis at $(0,1)$, continues to fall toward the x-axis (never touching it), etc.
Plan:
Plot some points $(x,(\displaystyle \frac{1}{3})^{x})$ and join with a smooth curve to graph $ f(x).$
Graph the line $ y=x.$
Reflect the points plotted earlier about the line $ y=x.$
Join these new points to graph $ g(x)=\log_{1/3}x $
From the graph, read the domains and ranges, $\left.\begin{array}{lll}
& domain & range\\
\hline f(x) & (-\infty,\infty) & (0,\infty)\\
g(x) & (0,\infty) & (-\infty,\infty)
\end{array}\right.$
