Question

find the inverse of the following function. Find the domain, range, and asymptotes of each function.

f(x)=3+1n(x+2)

Answer 1

I think you meant to type

f(x) = 3 + ln(x+2)

we can take logs of only positive numbers, so
x+2 > 0
x > -2

ln(a number) can be any real number.

domain: x > 2
range: f(x) any real number
asymptote: none

Answer 2

of course, there is a vertical asymptote at x = -2