6 Find the coordinates of the stationary point of the curve with equation $$( x + y - 2 ) ^ { 2 } = \mathrm { e } ^ { y } - 1$$ \(7 \quad\) A function f has domain \(\mathbb { R }\) and range \(\{ y \in \mathbb { R } : y \geq \mathrm { e } \}\) The graph of \(y = \mathrm { f } ( x )\) is shown.
\includegraphics[max width=\textwidth, alt={}, center]{5e475c96-6bbb-44fb-a411-706dac20e2d6-08_922_1108_447_466} The gradient of the curve at the point \(( x , y )\) is given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = ( x - 1 ) \mathrm { e } ^ { x }\)
Find an expression for \(\mathrm { f } ( x )\).
Fully justify your answer.