No, that is not correct. For one thing, in the original function, , when x= 4, y= 0. But with your function, , does not have a real number when x= 0. Also since the original function has limits on x, so should the inverse function.

As for x being "under the root", since in the original function x is squared, I can't see why you should expect the "opposite" of that, the square root of x, for the inverse function. But how did you get x- 12, rather than 12- x?