the equation becomes y = (x+3)^2.
replace y with x and x with y to get x = (y+3)^2
take the square root of both sides of the equation to get plus or minus sqrt(x) = y + 3
solve for y to get y = -3 plus or minus sqrt(x).
if they are inverse equations of each other, then the value of y in the original equation should be equal to the value of x in the inverse equation and the value of x in the original equation should be equal to the value of y in the inverse equation.
your original equation is y = (x+3)^2.
when x = 6, y = 9^2 = 81
when x = -6, y = (-3)^2 = 9
your coordinate pairs from the original equation are (6,81) and (-6,9)
your corresponding coordinate pairs in the inverse equations should be (81,6) and (9,-6).
your first inverse equation is y = -3 + sqrt(x).
when x = 81, y becomes equal to -3 + sqrt(81) which is equal to -3 + 9 which is equal to 6.
your coordinate pair is therefore (81,6) which is the inverse coordinate pair of (6,81) from the original equation.
your second inverse equation is y = -3 - sqrt(x).
when x = 9, y becomes equal to -3 - sqrt(9) which is equal to -3 - 3 which is equal to -6.
your coordinate pair is therefore (9,-6) which is the inverse coordinate pair of (-6,9).
you can see what's going on in the following graph:
the original equation is y = (x+3)^2.
the inverse equations are y = -3 + sqrt(x) and y = -3 - sqrt(x).
you can see that the inverse equation of y = -3 + sqrt(x) coresponds to the right side of the original equation of y = (x+3)^2.
you can also see that the inverse equation of y = -3 - sqrt(x) corresponds to the left side of the original equation of y = (x+3)^2.
note that the inverse equation of y = (x+3)^2 is actually x = (y+3)^2.
the rest is just solving for y in that equation.