Hmmmmm... doing the math i got the same answer, so i supose it is right.
if you want to show your work, i can dobble check to see if i did it the same way you did.
Note that the domain of is limited to because we cannot take the log of a negative number or 0 (well we can but then we get complex answers). The range is all the real numbers.
edit (more info): If you look at you may notice that the range is and that the domain is all the real numbers. If you compare that to the range and domain of you will see they've 'swapped' around. This is a property of all inverse functions. Furthermore functions and their inverses are reflections in the line