Answer
(a) $(2,\infty)$
(b) See graph.
(c) $(-\infty,\infty)$, $x=2$.
(d) $ f^{-1}(x)=5^{1-x}+2$
(e) $(-\infty,\infty)$, $(2,\infty)$.
(f) See graph.
Work Step by Step
(a) Given $f(x)=1-log_5(x-2)$, we can find its domain as $(2,\infty)$
(b) See graph.
(c) We can determine the range of $f$ as $(-\infty,\infty)$, asymptote(s) as $x=2$.
(d) Find the inverse $f(x)=1-log_5(x-2) \longrightarrow y=1-log_5(x-2) \longrightarrow x=1-log_5(y-2) \longrightarrow y=5^{1-x}+2 \longrightarrow f^{-1}(x)=5^{1-x}+2$
(e) We can find the domain of $f^{-1}$ as $(-\infty,\infty)$, range as $(2,\infty)$.
(f) See graph.