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Byju's Answer
Standard XII
Mathematics
Definition of Functions
ntThe functio...
Question
ntThe function f(x)=(x+1)/(x+1) can be written as sum of an even function g(x) and an odd function h(x). Then the value of g(0)+2 isn ntA) 1n ntB) 3n ntC) 5n ntD) 7n
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Q.
The function
f
(
x
)
=
x
+
1
x
2
+
1
can be written as the sum of an even function
g
(
x
)
and an odd function
h
(
x
)
. Then the value of
|
g
(
0
)
|
is ____.
Q.
The function
f
(
x
)
=
x
+
1
x
3
+
1
can be written as the sum of an even function
g
(
x
)
and an odd function
h
(
x
)
. Then the value of
|
g
(
0
)
|
is
Q.
Assertion :The function
f
(
x
)
=
∫
x
0
√
1
+
t
2
d
t
is an odd function and
g
(
x
)
=
f
′
(
x
)
is an even function. Reason: For a differentiable function
f
(
x
)
if
f
′
′
(
x
)
is an even function, then
f
(
x
)
is an odd function.
Q.
Assertion :If
f
(
x
)
=
∫
x
0
g
(
t
)
d
t
, where
g
is an even function and
f
(
x
+
5
)
=
g
(
x
)
, then
g
(
0
)
−
g
(
x
)
=
∫
x
0
f
(
t
)
d
t
Reason:
f
is an odd function.
Q.
Assertion :Let
f
(
x
)
=
tan
x
and
g
(
x
)
=
x
2
then
f
(
x
)
+
g
(
x
)
is neither even nor odd function. Reason: If
h
(
x
)
=
f
(
x
)
+
g
(
x
)
, then
h
(
x
)
does not satisfy the condition
h
(
−
x
)
=
h
(
x
)
and
h
(
−
x
)
=
−
h
(
x
)
.
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