ACJC Tutorial 3 Question 9

A graph with the equation \(y=\mathrm{f}(x)\) undergoes, in succession, the following transformations:

\(A\): A translation of \(1\) unit in the direction of the positive \(x\)- axis.

\(B\): A stretch parallel to the \(x\)- axis by factor \(\frac{1}{2}\).

\(C\): A reflection in the \(y\)- axis.

The equation of the resulting curve is \(y=\frac{2}{2{{x}^{2}}+2x+1}\). Determine the equation \(y=\mathrm{f}(x)\).