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

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+ | ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Rational Function

Let f : R → R...

Question

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

2 x

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 | x |

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

- 2 x

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 2 | x |

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

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

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

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

Suggest Corrections

Similar questions

Q. 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|

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

Q. Let

f : R \to R

be defined by

f (x) = 2 x + | x |

Then prove that

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

f : R \to R

is defined as

f (x) = 2 x + | x |

then

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

Q. Let

f : R \to R

be defined by

f (x) = 2 x + | x |

. Then

f (2 x) + f (- x) - f (x)

Join BYJU'S Learning Program

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

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

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

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