Reverse transformation (given transformed point)

Given a point on a transformed curve y=g(f(x)), find the corresponding original point on y=f(x).

1 questions

CAIE P1 2021 November Q2
2 The graph of \(y = \mathrm { f } ( x )\) is transformed to the graph of \(y = \mathrm { f } ( 2 x ) - 3\).
  1. Describe fully the two single transformations that have been combined to give the resulting transformation.
    The point \(P ( 5,6 )\) lies on the transformed curve \(y = \mathrm { f } ( 2 x ) - 3\).
  2. State the coordinates of the corresponding point on the original curve \(y = \mathrm { f } ( x )\).