Answer
(a) $(-2,\infty)$.
(b) See graph.
(c) range $(-\infty,\infty)$, V.A. $x=-2$.
(d) $ f^{-1}(x)=3^{x-3}-2$
(e) domain $(-\infty,\infty)$, range $(-2,\infty)$.
(f) See graph.
Work Step by Step
(a) Given $f(x)=3+log_3(x+2)$, we can find the domain $x+2\gt0$ or $(-2,\infty)$.
(b) See graph.
(c) From the graph, we can determine the range $(-\infty,\infty)$, asymptote(s) V.A. $x=-2$.
(d) $f(x)=3+log_3(x+2)\Longrightarrow y=3+log_3(x+2)\Longrightarrow x=3+log_3(y+2) \Longrightarrow y=3^{x-3}-2 \Longrightarrow f^{-1}(x)=3^{x-3}-2$
(e) For $ f^{-1}(x)$, we can find the domain $(-\infty,\infty)$, range $(-2,\infty)$.
(f) See graph.
