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)

-1 - 1

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