If you have to find the inverse your domain and range of the original function swap around. So in the case of this question, you got a (+/-)sqrt(3x+4),
you set 3x+4 >(or equal to) 0
3x >(or equal to) -4
x >(or equal to) -4/3
which is the same as the range on your original function. Since the domain on your original function is less than or equal to 0, the range of your inverse must be less than or equal to 0, which I think explains the negative sign (any value obtained from subbing in x values will be less than 0 or equal to it).
If you don't know what to do, I am assuming you get access to a graphical calculator in your exam - just remember the real inverse function will be a reflection in the line y=x. So if you draw all the graphs, the one which reflects the original f(x) function in y=x will be the correct inverse.