Answer
(a) $(-\infty,\infty)$.
(b) See graph
(c) $(-\infty,0)$, $y=0$.
(d) $f^{-1}(x)=log_3(-x)-1$.
(e) $(-\infty,0)$, $(-\infty,\infty)$.
(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 $f(x)=-3^{x+1}$
(c) We can determine the range as $(-\infty,0)$ and asymptote(s) as $y=0$.
(d) We can find $f^{-1}(x)=log_3(-x)-1$. In short $x=-3^{y+1}\longrightarrow y=log_3(-x)-1$
(e) We can find the domain of $f^{-1}(x)$ as $(-\infty,0)$ and range as $(-\infty,\infty)$.
(f) See graph.
