2015 IJC P1 Q8

A curve with equation \(y=\mathrm{f}(x)\) undergoes the following sequence of transformation.

\(\qquad A\): A translation of \(3\) units in the positive \(y\)-direction.
\(\qquad B\): A translation of \(2\) units in the positive \(x\)-direction.
\(\qquad C\): A stretch with scale factor \(2\) parallel to the \(x\)-axis.

The resulting curve has equation \(y=\mathrm{g}(x)\) where \(\mathrm{g}(x)=2-\frac{4}{3x-7}\). Find \(\mathrm{f}(x)\) in terms of \(x\). [3]

Another curve with equation \(y=\frac{1}{\mathrm{f}(x)}\) undergoes the same sequence of transformations \(A\), \(B\) and \(C\).
Will the equation of the resulting curve be\(y=\frac{1}{\mathrm{g}(x)}\)? Justify your answer[1]