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प्रश्न
Let f : R → R be defined by f(x) = 2x + |x|. Then f(2x) + f(−x) − f(x) =
विकल्प
(a) 2x
(b) 2|x|
(c) −2x
(d) −2|x|
उत्तर
(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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