Question

find the inverse of function f(x)=4-2ln(x+1). state domain, range and any asymptotes of both

Answer 1

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

domain: x > -1
range : y is any real number
asymptote: x = -1

for the inverse:
interchange x and y variables
x = 4 - 2ln(y+1)
2ln(y+1) = 4-x
ln (y+1) = (4-x)/2
y+1 = e^((4-x)/2)
y = e^((4-x)/2) - 1

domain: x is any real number
range y > -1
asymptote : y = -1