The domain is restricted when
is not defined. The only time this could be undefined is if the denominator is zero. Find the domain so that the denominator is never zero.
To find the range consider what the value of f(x) is when x gets close to the limits of the domain and then consider if there is any reason why a number between the limits of the domain that would have a value of f(x) more extreme than f(x) at the limits of the domain.
The inverse of the function contains a log with a fraction in it. Do what you did with f(x) to find the domain but this time there are 2 ways a log can be not defined.
is not defined when is less than or equal to zero, and it is not defined when b=0