Answer
(a) domain $(-\infty,\infty)$ and range $(2,\infty)$.
(b) $f^{-1}(x)=log_3(x-2)$, domain $(2,\infty)$ and range $(-\infty,\infty)$.
Work Step by Step
(a) Given $y=3^x+2$, we can find its domain $(-\infty,\infty)$ and range $(2,\infty)$.
(b) $3^x=y-2$, $x=log_3(y-2)$, thus the inverse is $f^{-1}(x)=log_3(x-2)$ with domain $(2,\infty)$ and range $(-\infty,\infty)$.
