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$I f f (x) = - | x |, t h e n (f o f o f) (x) + (f o f o f) (- x) =$

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$2 f$

$2 | f |$

$- | f |$

$- 2 f$

answer is C.

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Detailed Solution

$\begin{array}{l} f (x) = - | x | \\ f o f o f (x) = f (f (f (x))) = f (| - | x | |) \\ = f (| x |) \\ = - | x | \\ f o f o f (- x) = - | - x | = - | x | \\ ∴ f o f o f (x) + f o f o f (- x) = - | x | - | x | \\ = - 2 | x | \\ = 2 f \end{array}$

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