The inverse of the function y = 9 - x 2, for all values x ≥ 3, is where x can take values

show your work.

Inverse of y=9-x²; you just replace x by y and y by x: x=9-y².

And the value of y:    y² = 9-x  and y =√(9 - x) [this is the inverse function]

f⁻¹(x) = √(9-x): CONDITION :  (9-x) >=0, that means x< or = 9
 
Answer as per your problem:

The inverse of the function y = 9 - x 2, for all values x ≥ 3, is y =√(9 - x), where x can take values x<=9.