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Byju's Answer
Standard XII
Mathematics
Constant Function
If fx + 2a = ...
Question
If f(x + 2a) = f(x - 2a), then f(x) is,
A
a periodic function with period 4a
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B
a periodic function with period 2a
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C
a periodic function with indeteminate period
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D
a non periodic function
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Solution
The correct option is
A
a periodic function with period 4a
∵
f
(
x
+
2
a
)
=
f
(
x
−
2
a
)
This ia the value at
x
=
−
2
a
f
(
x
−
2
a
)
is the value at
x
=
2
a
∴
Distance between the point and X where values of function are equal
=
2
a
+
2
a
=
4
a
∴
f is a periodic function with period
4
a
.
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0
Similar questions
Q.
The function
f
(
x
)
=
|
sin
4
x
|
+
|
cos
2
x
|
, is a periodic function with period
Q.
If
f
(
x
)
is an odd periodic function with period
2
, then
f
(
4
)
equals
Q.
If
f
′
(
x
)
=
1
−
2
sin
2
x
f
(
x
)
,
f
(
x
)
>
0
,
∀
x
∈
R
and
f
(
0
)
=
1
. Then
f
(
x
)
is a periodic function with the period
Q.
If
f
(
x
)
is a periodic function of the period
k
then
f
(
k
x
+
a
)
,
where
a
is a constant, is a periodic function of the period
Q.
Assertion :If
f
(
x
)
is a non-negative continuous function such that
f
(
x
)
+
f
(
x
+
1
2
)
=
1
then
∫
2
0
f
(
x
)
d
x
=
1
Reason:
f
(
x
)
is a periodic function having period
1
.
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