Answer
(a) $(-\infty,\infty)$.
(b) See graph
(c) $(4,\infty)$, $y=4$.
(d) $f^{-1}(x)=3ln(\frac{x-4}{2})$.
(e) $(4,\infty)$, $(-\infty,\infty)$.
(f) See graph.
Work Step by Step
(a) Use the domain requirement(s) for the function, we have the domain as $(-\infty,\infty)$.
(b) See graph for $f(x)=2e^{x/3}+4$
(c) We can determine the range as $(4,\infty)$ and asymptote(s) as $y=4$.
(d) We can find $f^{-1}(x)=3ln(\frac{x-4}{2})$. In short $x=2e^{y/3}+4\longrightarrow y=3ln(\frac{x-4}{2})$
(e) We can find the domain of $f^{-1}(x)$ as $(4,\infty)$ and range as $(-\infty,\infty)$.
(f) See graph.
