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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| - Mathematics

MCQ

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

Options

  • (a) 2x

  • (b) 2|x|

  • (c) −2x

  • (d) −2|x|

     
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Solution

(b) 2|x|

f(x) = 2x + |x|
Then, f(2x) + f(−x) − f(x)

\[= 2\left( 2x \right) + 2\left| x \right| + \left( - 2x \right) + \left| - x \right| - 2x + \left| x \right|\]
\[ = 4x - 2x - 2x + 2\left| x \right| + \left| - x \right| - \left| x \right|\]
\[ = 0 + 2\left| x \right| + \left| x \right| - \left| x \right|\]
\[ = 2\left| x \right|\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Q 15 | Page 43
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