what is the domain of f(x)=-ln(-x) and the inverse

Answer 1

ln(x) has domain x > 0
so, -ln(-x) has domain -x > 0 or x < 0, but its range is all real y

y = -ln(-x)
-y = ln(-x)
e^(-y) = -x
x = -e^(-y)

f^-1(x) = -e^-x

Note that the domain of f^-1 is all reals, but the range is y < 0