(a) agree with your domain.

for the range, consider the first domain interval ... as , and as , ... the range of the log function over this interval is .

now consider the other interval of the domain ... as , and as , ... the range of the log function over this interval is .

I'd say the range is all reals except y = 0

(b) inverse ...

(c) ... wouldn't the range of the inverse be the domain of the original function?