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  4. If f: R → R is defined by f(x) = 3x + |x| , then f(2x) - f (- x) - 6x =

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Q. If f : R $\to$ R is defined by f(x) = 3x + |x| , then f(2x) - f (- x) - 6x =

Relations and Functions

Solution:

f (x) = 3x+ | x |
$\therefore $ f (2x) - f (-x) - 6x
=6x+ | 2x | -3(-x)- | -x | -cx
= 3x + 2 | x | - | x | ($\because$| x |=| -x |)
= 3x + | x |= f (x)