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 $2^{x}$ is always above the x-axis,
rises from the far left slowly to pass through (0,1) on the y-axis, continues to rise through points $(1,2^{1}),(2,2^{2})$, etc.
Plan:
Plot some points $(x,2^{x})$ 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_{2}x $
From the graph, read the domains and ranges,
$\left.\begin{array}{ccc}
& domain & range\\
\hline f(x) & (-\infty,\infty) & (0,\infty)\\
g(x) & (0,\infty) & (-\infty,\infty)
\end{array}\right.$
