Methods 3/4 Transformations and Matrices Question

[Immune_Sushi]

Hi ,

In regards to Transformations and Matrices (Ill try to keep this question as condensed as possible):

When we "transform" a function, we usually state the dilation, reflections then the transformations right?.

Similarly, when reverting a "transfromed" function back into an "original' function, (see example below), we usually state the translations then  dilations and reflections.

Im wondering if the method below is correct:

so, when we are transforming back to



(working out)

Spoiler

       is the image, so we turn in into

Therefore    which is equal to and 

Therefore:
There is a
-vertical translation of 2 in the positive y direction
-horizontal translation of 7 in the positive x direction
-refection in the x-axis
-dilation factor of 6 away from the y axis
-dilation factor of 0.5 away from the x axis

 

My main problem is that when the question asks you to represent these transformations on this particular matrix;



I've been taught that for reverting to the "oringal" function it has to be translations first, then reflection and dilations.
This matrix restricts and forces it  to  state the dilations and reflections first, then transformations. Is there a way to overcome this problem?
(And for people who have completed VCE methods, has this shown up on your SAC's or the Exams?)

What do you think?