Answer
The function is even.
Work Step by Step
$f(-x) = |-x| \cos{(-x)} $
$\because |-x| = |x| \hspace{10pt} \& \text{ } \cos{(-x)} = \cos{x}$
$\therefore f(-x) =|x| \cos{x} = f(x)$
The function is even.
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