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Byju's Answer
Standard XII
Mathematics
Polynomial Functions
State the whe...
Question
State the whether given statement is true or false
If
f
(
x
)
=
x
+
1
x
−
1
,
then
f
(
x
)
+
f
(
1
x
)
=
0
A
True
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B
False
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Solution
The correct option is
A
True
f
(
x
)
=
x
+
1
x
−
1
f
(
1
x
)
=
1
x
+
1
1
x
−
1
=
1
+
x
1
−
x
=
−
1
+
x
x
−
1
Hence,
f
(
x
)
+
f
(
1
x
)
=
x
+
1
x
−
1
−
x
+
1
x
−
1
=
0
Suggest Corrections
0
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State whether the given statement is true or false
If f(x) satisfies the relation, f(x+y)=f(x)+f(y) for all
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State the whether given statement is true or false
If
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State whether the given statement is true or false
If
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+
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(
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1
−
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2
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.
.
.
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<
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Q.
Assertion :Statement 1:
F
(
x
)
=
∫
x
1
log
t
1
+
t
+
t
2
d
t
then
F
(
x
)
=
−
F
(
1
/
x
)
Reason: Statement 2: If
F
(
x
)
=
∫
x
1
log
t
t
+
1
d
t
then
F
(
x
)
+
F
(
1
/
x
)
=
(
1
/
2
)
(
log
x
)
2
Q.
Assertion :If
f
(
x
)
=
∫
x
1
l
n
t
d
t
1
+
t
+
t
2
(
x
>
0
)
then
f
(
x
)
=
−
f
(
1
x
)
Reason: If
f
(
x
)
=
∫
x
1
l
n
t
d
t
t
+
1
,
then
f
(
x
)
+
f
(
1
x
)
=
1
2
(
l
n
x
)
2
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