Answer
(a) $(4,\infty)$.
(b) See graph
(c) $(-\infty,\infty)$, $x=4$.
(d) $f^{-1}(x)=10^{x-2}+4$.
(e) $(-\infty,\infty)$, $(4,\infty)$.
(f) See graph.
Work Step by Step
(a) Use the domain requirement(s) for the function $x-4\gt0$, we have $x\gt4$ or $(4,\infty)$.
(b) See graph for $f(x)=log(x-4)+2$
(c) We can determine the range as $(-\infty,\infty)$ and asymptote(s) as $x=4$.
(d) We can find $f^{-1}(x)=10^{x-2}+4$. In short $x=log(y-4)+2\longrightarrow y=10^{x-2}+4$
(e) We can find the domain of $f^{-1}(x)$ as $(-\infty,\infty)$ and range as $(4,\infty)$.
(f) See graph.
