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$I f f; R \to R i s d e f i n e d b y f (x) = 2 x + | x |, t h e n f (3 x) - f (- x) - 4 x =$

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$2 f (x)$

$f (x)$

$f (- x)$

$f (1)$

answer is D.

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Detailed Solution

$\begin{array}{l} f (x) = 2 x + | x | t h e n \\ f (3 x) - f (- x) - 4 x = 2 (3 x) + | 3 x | - (2 x + | - x |) - 4 x \\ = 6 x + 3 | x | + 2 x - | x | - 4 x \\ = 4 x + 2 | x | \\ = 2 (2 x + | x |) = 2 f (x) \end{array}$

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