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Byju's Answer
Standard XI
Mathematics
Absolute Value Function
Let f : R ...
Question
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|
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Solution
(b) 2|x|
f(x) = 2x + |x|
Then, f(2x) + 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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