g(x) is formed after ABC , so by working backwards

Before C : g(x) = 1/2 g(x)
since after C is x2 , before C would be ÷2

Before B : 1/2 g(x) = 1/2 g(-x)
since it’s reflection about y-axis , it means it’s reflected towards the y-axis , where the graph reflected will be the reflection of the graph where x is >0

think of it as a mirror where y-axis is the vertical mirror and you are the graph , YOU need to be reflected , so you know how reflections are opposite ( like when u move left , mirror moves right from its’ perspective ) , so if the actual side shows a curve going up as x increases , the reflected would be the curve going up as x DECREASES ( its hard to explain so I’m so sorry if it’s confusing )

Before A : 1/2 g(-x+1)
since the final is g(x) , you wanna get rid of the +1 in (x+1) so u gotta move to the negative side (-1) to get rid of the +1

Not the best at explaining but i hope it helps abit