Answer
(a) $(3,\infty)$
(b) See graph
(c) $(-\infty,,\infty)$, $x=3$.
(d) $f^{-1}(x)=e^{x}+3$
(e) $(-\infty,,\infty)$, $(3,\infty)$.
(f) See graph.
Work Step by Step
(a) Use the domain requirement(s) for the function $x-3\gt0$, we have $x\gt3$ or $(3,\infty)$
(b) See graph for $f(x)=ln(x-3)$
(c) We can determine the range as $(-\infty,,\infty)$ and asymptote(s) as $x=3$.
(d) We can find $f^{-1}(x)=e^{x}+3$
(e) We can find the domain of $f^{-1}(x)$ as $(-\infty,,\infty)$ and range as $(3,\infty)$.
(f) See graph.
