2021 SAJC P1 Q2(b)

A curve undergoes the transformations \(A\), \(B\) and \(C\) in succession. The transformations \(A\), \(B\) and \(C\) are given as follows:

\(A\): Translate 1 unit in the positive \(x\)- direction;

\(B\): Scale parallel to \(x\)-axis by a scale factor of \(5\);

\(C\): Reflect in the \(y\)-axis.

The equation of the resulting curve is \(y={{e}^{x-2}}-x\). Determine the equation of the original curve.[3]