- In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{08291ac1-bdd4-4241-8959-7c89318fa5eb-26_613_729_386_667}
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\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of the curve with equation
$$y = | 2 - 4 \ln ( x + 1 ) | \quad x > k$$
where \(k\) is a constant.
Given that the curve
- has an asymptote at \(x = k\)
- cuts the \(y\)-axis at point \(A\)
- meets the \(x\)-axis at point \(B\)
as shown in Figure 2,
- state the value of \(k\)
- find the \(y\) coordinate of \(A\)
- find the exact \(x\) coordinate of \(B\)
- Using algebra and showing your working, find the set of values of \(x\) such that
$$| 2 - 4 \ln ( x + 1 ) | > 3$$