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Not exactly, why are you equating the equation while finding the inverse?
This is what I did.
To find H inverse
Let y = h(x)
h(x)= 9-(x-3)^2
h(x)-9= (x-3)^2
*root*h(x)-9= x-3
[*root*h(x)-9]+3 = x
H inverse = [*root*h(x)-9]+3 where as yours and the MS's is "9-x" instead of "x-9"
EDIT: I undestand what you did, but why is my method wrong?
"To find H inverse
Let y = h(x)
h(x)= 9-(x-3)^2
h(x)-9= - (x-3)^2
The '-'... U omitted it! Correction in red