the questino is

A)find domain and range

b)find domain and range of inverse function

c)Find an explicit formula for the inverse function as a function of x.

$\displaystyle f(x) (x-2)^2-9 x is bigger than or equal to 4$

a)domain of original function is [4, infinity)

How do I find the range?

b)domain of inverse function is range of original function, range of inverse function is domain of original function so [4, infinity)

c) the formula for the inverse function is

$\displaystyle f(x)=(x-2)^2-9$

$\displaystyle x=(f(x)-2)^2-9$

$\displaystyle x+9 = (f(x)-2)^2$

$\displaystyle \sqrt{x+9} = f(x)-2$

$\displaystyle 2+\sqrt{x+9} = f(x) $

i would think that the range would be [9, infinity), since 9 would be the lowest number than can still make the square root non negative, but the book's answer says the range of the original function/domain of inverse is [-5, infinity) does this have something to do with the restricted domain? if so, what do I do to get this range?