7. For the constant \(k\), where \(k > 1\), the functions f and g are defined by
$$\begin{aligned}
& \mathrm { f } : x \mapsto \ln ( x + k ) , \quad x > - k ,
& \mathrm {~g} : x \mapsto | 2 x - k | , \quad x \in \mathbb { R } .
\end{aligned}$$
- On separate axes, sketch the graph of f and the graph of g .
On each sketch state, in terms of \(k\), the coordinates of points where the graph meets the coordinate axes.
- Write down the range of f.
- Find \(\mathrm { fg } \left( \frac { k } { 4 } \right)\) in terms of \(k\), giving your answer in its simplest form.
The curve \(C\) has equation \(y = \mathrm { f } ( x )\). The tangent to \(C\) at the point with \(x\)-coordinate 3 is parallel to the line with equation \(9 y = 2 x + 1\).
- Find the value of \(k\).