| Exam Board | AQA |
|---|
| Module | Further Paper 1 (Further Paper 1) |
|---|
| Session | Specimen |
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| Marks | 3 |
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| Topic | Hyperbolic functions |
|---|
12 The function \(\mathrm { f } ( x ) = \cosh ( \mathrm { i } x )\) is defined over the domain \(\{ x \in \mathbb { R } : - a \pi \leq x \leq a \pi \}\), where \(a\) is a positive integer.
By considering the graph of \(y = [ f ( x ) ] ^ { n }\), find the mean value of \([ f ( x ) ] ^ { n }\), when \(n\) is an odd positive integer.
Fully justify your answer.
[0pt]
[3 marks]