You are given that \(g f ( x ) = | 3 x - 1 |\) for \(x \in \mathbb { R }\).
Given that \(f ( x ) = 3 x - 1\), express \(g ( x )\) in terms of \(x\).
State the range of \(g f ( x )\).
Solve the inequality \(| 3 x - 1 | > 1\). [0pt]
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\section*{2. In this question you must show detailed reasoning.}
Express \(8 \cos x + 5 \sin x\) in the form \(R \cos ( x - \alpha )\), where \(R\) and \(\alpha\) are constants with \(R > 0\) and \(0 < \alpha < \frac { 1 } { 2 } \pi\).
Hence solve the equation \(8 \cos x + 5 \sin x = 6\) for \(0 \leqslant x < 2 \pi\), giving your answers correct to 4 decimal places. [0pt]
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