parent function with Inverse function

1. Now consider the parent function P(x) = x2, and let g(x) = 4(x-1)2 + 8.

(A) Explain step-by-step, graphing/labeling (on graph paper!) the parent, each intermediate function, if we do transformations in these two orders: (You will have to figure out the exact transformations in each case.)

   (i)Horizontal shift then vertical stretch then vertical shift;  (ii)Horizontal shift then vertical shift then  vertical stretch.

(B) (i) Explain how you can cut the domain of our g(x) so that at least part of it has an inverse function (I.e. passes the horizontal line test).

  (ii) Now find the equation of the INVERSE function of our g(x).