(10分)中四 maths

this question is little difficult and be careful.
since the 4 kind of translation occurred.

i use the f(x) oriented method (i create this name :P), always treat the function and the x-axis only,


f(x) ; this is your original function
f(x-2/3) ; translate it to right by 2/3 unit, now it is your new function
f( -3[x-2/3]); shorter it by 3 time and reflect on x=2/3
f( -3 x+2 ) +2 ; left up the function by 2 unit
-2 [ f(-3x+2) +2 ]; enlarge the function by 2 and reflect it respect to x-axis
=g(x)