6.
$$\mathrm { f } ( x ) = \mathrm { e } ^ { 3 x + 1 } - 2 , \quad x \in \mathbb { R } .$$
- State the range of f .
The curve \(y = \mathrm { f } ( x )\) meets the \(y\)-axis at the point \(P\) and the \(x\)-axis at the point \(Q\).
- Find the exact coordinates of \(P\) and \(Q\).
- Show that the tangent to the curve at \(P\) has the equation
$$y = 3 \mathrm { e } x + \mathrm { e } - 2 .$$
- Find to 3 significant figures the \(x\)-coordinate of the point where the tangent to the curve at \(P\) meets the tangent to the curve at \(Q\).