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?
I got x-12 by subtracting 12 from both sides. I then put the whole of both sides over -3 to get rid of the -3 which multiplies the brackets on the right, then put the both sides under a root to un-square the bracket. Tried replacing (x-1)^2 with (x-1)(x-1) and multiplying out and got into a bit of a pickle.
This is how I do it:
Now here we have a problem....we don't know which square root to take, yet. More on that later.
now when x is 0, y is 9, so this helps us decide which square root we need:
. Wrong one.
So it ought to be that:
Just as a safeguard, let's see if :
then put the both sides under a root to un-square the bracket. Tried replacing (x-1)^2 with (x-1)(x-1) and multiplying out and got into a bit of a pickle.