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

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

y = 4-2ln(x+1)

Domain is x > -1

Range y is any real number.

Asympotate x = -1

Replace the x and y.

x = 4-2ln(y+1)

Add 2ln(y+1) to each side.

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

x+2ln(y+1) = 4

Subtract x from each side.

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

2ln(y+1) = 4-x

Divide to each side by 2.

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

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

Raise by e on each side.

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

Subtract 1 from each side.

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

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

Domain is x is any real number.

Range is y > -1

Asympotate y = -1