2. Given that
$$\mathrm { f } ( x ) = 2 \mathrm { e } ^ { x } - 5 , \quad x \in \mathbb { R }$$
- sketch, on separate diagrams, the curve with equation
- \(y = \mathrm { f } ( x )\)
- \(y = | \mathrm { f } ( x ) |\)
On each diagram, show the coordinates of each point at which the curve meets or cuts the axes.
On each diagram state the equation of the asymptote.
- Deduce the set of values of \(x\) for which \(\mathrm { f } ( x ) = | \mathrm { f } ( x ) |\)
- Find the exact solutions of the equation \(| \mathrm { f } ( x ) | = 2\)