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Let \(f\) be a function \(f: \mathbb{N} \rightarrow \mathbb{N}\) defined by \(f(x) = 3x + 2\), \(x \in \mathbb{N}\).
(i) Find the images of \(1\), \(2\), \(3\).
(ii) Find the pre-images of \(29\), \(53\).
(iii) Identify the type of function.
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