Sketch the graphs of \(y = 1 + \mathrm { e } ^ { 2 x }\) and \(y = | x - 4 |\) on the same diagram.
The two graphs meet at the point \(P\) .
Show that the \(x\)-coordinate of \(P\) satisfies the equation \(x = \frac { 1 } { 2 } \ln ( 3 - x )\) .
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Use an iterative formula, based on the equation in part (b), to find the \(x\)-coordinate of \(P\) correct to 3 significant figures. Use an initial value of 0.45 and give the result of each iteration to 5 significant figures.