Let f - - be defined by fx - 2x- -x- Then f2x- f-x- fx is

F(x) = 2x+ |x| f(2x)= 2(2x)+ |2x| ⇒ f(2x) = 4x+ |2x| f( x)= 2( x)+ | x| ⇒ f( x) = 2x+ |x| ∴ f(2x)+ f( x) f(x) = 4x+ |2x| 2x+ |x| 2x |x| =|2x|=2|x| nb ...

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Byju's Answer

Standard XII

Mathematics

Definition of Functions

Let f : ℝ→ℝ b...

Question

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

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

$f (2 x) = 2 (2 x) + | 2 x | \Rightarrow f (2 x) = 4 x + | 2 x |$

$f (- x) = 2 (- x) + | - x | \Rightarrow f (- x) = - 2 x + | x |$

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

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

The correct option is B 2|x|f(x)=2x+|x| f(2x)=2(2x)+|2x|⇒f(2x)=4x+|2x| f(−x)=2(−x)+|−x|⇒f(−x)=−2x+|x| ∴f(2x)+f(−x)−f(x) =4x+|2x|−2x+|x|−2x−|x| =|2x|=2|x|

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

The correct option is B $2 | x |$
$f (x) = 2 x + | x |$

$f (2 x) = 2 (2 x) + | 2 x | \Rightarrow f (2 x) = 4 x + | 2 x |$

$f (- x) = 2 (- x) + | - x | \Rightarrow f (- x) = - 2 x + | x |$

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