Find the inverse of the function h (x)=x^2+6x+9 and indicate restrictions on the domain, if any

First of all, recognize that h(x) = x^2 + 6x + 9 = (x + 3)^2.

1) Replace h(x) with y:  y = (x+3)^2
2) Interchange x and y:  x = (y+3)^2
3) Solve this new equation for y.  Take the sqrt of both sides:

plus or minus sqrt(x) = y+3, so y = -3 plus or minus sqrt(x)
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4) replace y with  f     (x).        f    (x) = -3 plus or minus sqrt(x) (answer)