Question

How do find the inverse function for this problem:

f(x) = -(x+3)^2, x is greater than or equal to 3

I know the first thing you do is switch the variables, so it looks like this:
x = -(y+3)^2
Then expand:
x = -y^2-6y-9
And solve for y:
x + 9 = -y^2-6y

I get a little confused after that with y. Help please? Thank you very much!

Answer 1

At the step where you have x = -(y+3)^2, you should take the square root of both sides.

sqrt(x) = -(y+3)
-sqrt(x) = y+3
-sqrt(x) - 3 = y