Answer
(a) $(-\infty,\infty)$.
(b) See graph.
(c) range $(4,\infty)$, H.A. $y=4$.
(d) $ f^{-1}(x)=3log_2(x-4)$
(e) domain $(4,\infty)$, range $(-\infty,\infty)$.
(f) See graph.
Work Step by Step
(a) Given $f(x)=2^{x/3}+4$, we can find the domain $(-\infty,\infty)$.
(b) See graph.
(c) From the graph, we can determine the range $(4,\infty)$, asymptote(s) H.A. $y=4$.
(d) $f(x)=2^{x/3}+4\Longrightarrow y=2^{x/3}+4\Longrightarrow x=2^{y/3}+4 \Longrightarrow y=3log_2(x-4) \Longrightarrow f^{-1}(x)=3log_2(x-4)$
(e) For $ f^{-1}(x)$, we can find the domain $(4,\infty)$, range $(-\infty,\infty)$.
(f) See graph.
