Answer
Domain: $\mathbb{R}$.
Range: $(0,\infty)$
Graph:
Work Step by Step
The graph of this function is obtained from $f_{1}(x)=e^{x}$,
by vertically stretch it by factor 2 (doubling the y-coordinates),
AND
by horizontally stretching it by factor 2 (doubling the the x-coordinates).
AND
reflecting it over the y-axis
Graph, with a dashed line, the graph of $f_{1}(x)=e^{x}$,
as instructed in the solution of exercise 47$:$
...Graphing $f_{1}(x)=e^{x}$ ,
... The base is $e\approx 2.718\gt 1$, so the graph rises on the whole domain.
... Asymptote is the x-axis.
... To the far left, the graph nears but does not cross the asymptote.
... The graph passes through the points
... $(-1,\displaystyle \frac{1}{e}),(0,1),(1,e),(2,e^{2})$, and so on.
... Plot these points and join with a smooth curve.
Then, for each of the points used for graphing $f_{1}$
perform the above transformations (double both coordinates, reflect across y)
plot the new points,
and join with a smooth curve (red on the image).
The asymptote remains the x-axis (double of zero is zero).
