Let f - R - R be defined by f x -2 x - x - - Then f 2 x - f - x - f x -A- -2 x- -2- x -C- 2 xD- 2- x -

The correct option is D 2|x| f(x) = x+|x| Then, f(x) + f( x) f(x) = 2 (2x) + 2|x| + ( 2x) + | x| 2x + |x| = 4x 2x 2x + 2|x| + | x| |x| = 0 + 2|x| + ...

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Byju's Answer

Standard XII

Mathematics

Definition of Functions

Let f : R → R...

Question

Let $f : R \to R$ be defined by $f (x) = 2 x + | x |$ . Then $f (2 x) + f (- x) - f (x) =$

$2 x$

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$2 | x |$

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$- 2 x$

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$- 2 | x |$

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Solution

The correct option is B
$2 | x |$

$f (x) = x + | x |$
Then, $f (x) + f (- x) - f (x)$
$= 2 (2 x) + 2 | x | + (- 2 x) + | - x | - 2 x + | x | = 4 x - 2 x - 2 x + 2 | x | + | - x | - | x | = 0 + 2 | x | + | x | - | x | = 2 | x |$

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

The correct option is B 2|x| f(x)=x+|x| Then, f(x)+f(−x)−f(x) =2(2x)+2|x|+(−2x)+|−x|−2x+|x|=4x−2x−2x+2|x|+|−x|−|x|=0+2|x|+|x|−|x|=2|x|

Let $f : R \to R$ be defined by $f (x) = 2 x + | x |$ . Then $f (2 x) + f (- x) - f (x) =$

The correct option is B
$2 | x |$

$f (x) = x + | x |$
Then, $f (x) + f (- x) - f (x)$
$= 2 (2 x) + 2 | x | + (- 2 x) + | - x | - 2 x + | x | = 4 x - 2 x - 2 x + 2 | x | + | - x | - | x | = 0 + 2 | x | + | x | - | x | = 2 | x |$