Q. 15

# Mark the correct alternative in the following:

Let f : R → r be defined by f(x) = 2x + |x|. Then f(2x) + f(-x) – f(x) =

A. 2x

B. 2 |x|

C. -2 x

D. -2 |x|

Answer :

f(2x)=2(2x)+|2x|=4x+2|x|

f(-x)=2(-x)+|-x|

f(2x)+f(-x)-f(x)=4x+2|x|-2x+|-x|-(2x+|x|)

=4x+2|x|-2x+|x|-2x-|x|=2|x|

Option B is correct..

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