find inverse of f(x)=4-2ln(x+1) determine domain any asymptotes and range for both

Question

I,ve tried three different ways and got three different answers  could you lead me down the right path?

Answer 1

f(x)=4-2ln(x+1)

y = 4 - 2ln( x + 1 ) ⇒ x + 1 > 0 ⇒ x > - 1

D: ( - 1, + infinitive )

R: all real numbers ( - infinitive, + infinitive )

vertical assymptote x = -1

inverse function

x = 4 - 2ln( y + 1)

2ln( y + 1) = 4 - x

ln( y + 1 ) = ( 4 - x )/2

e^((4 - x)/2) = y + 1

y = e^((4 - x)/2) - 1

D: ( - infinitive, + infinitive )

R: ( - 1, + infinitive)

horisontal asymptote y = - 1

Answer 2

I thank you very much -  had the domain, range and asymptote for the first and I knew x and y were interchanged to come up with the inverse.  I also knew domain of one = range of other and range of first = domain of other, but couldn't come up with the other.