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)