Question:
Let f : R → R be defined by f(x) = 2x + |x|. Then f(2x) + f(−x) − f(x) =
(a) 2x
(b) 2|x|
(c) −2x
(d) −2|x|
Solution:
(b) 2|x|
f(x) = 2x + |x|
Then, f(2x) + f(−x) − f(x)
$=2(2 x)+2|x|+(-2 x)+|-x|-2 x+|x|$
$=4 x-2 x-2 x+2|x|+|-x|-|x|$
$=0+2|x|+|x|-|x|$
$=2|x|$
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