Question

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

f(x)=In(x+1)+1
Please show work

Answer 1

original:

y = ln(x+1) + 1

inverse:
x = ln(y+1) + 1
x-1 = ln(y+1)

solving for y ....
y+1 = e^(x-1)
y = e^(x-1) - 1
or
f^-1 (x) = e^(x-1) - 1