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Standard XII
Mathematics
Symmetric Relations
35. Let h(x) ...
Question
35. Let h(x) = f(x)-1 . If f(x)+f(1-x) =2 for all x benlongs to R ,then h(x) is symmetric about
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Q.
Let f be a differentiable function such that
f
(
1
)
=
2
and
f
′
(
x
)
=
f
(
x
)
for all
x
∈
R
. If
h
(
x
)
=
f
(
f
(
x
)
)
, then
h
′
(
1
)
is equal to :
Q.
Let
f
(
x
)
=
x
2
−
1
x
2
and
g
(
x
)
=
x
−
1
x
,
x
∈
R
−
−
1
,
0
,
1
. If
h
(
x
)
=
f
(
x
)
g
(
x
)
then the local minimum value of
h
(
x
)
is:
Q.
Let
f
be a differentiable function such that
f
(
1
)
=
2
and
f
′
(
x
)
=
f
(
x
)
for all
x
∈
R
. If
h
(
x
)
=
f
(
f
(
x
)
)
, then
h
′
(
1
)
is equal to :
Q.
Let
f
(
x
)
=
[
x
[
x
]
]
,
g
(
x
)
=
[
x
[
1
x
]
]
and
h
(
x
)
=
[
[
x
]
x
]
,
, then
lim
x
→
2
−
f
(
x
)
+
lim
x
→
1
2
+
g
(
x
)
+
lim
x
→
2
+
h
(
x
)
=
Q.
Let
f
(
x
)
=
x
2
+
1
x
2
and
g
(
x
)
=
x
−
1
x
,
x
∈
R
−
−
1
,
0
,
1
. If
h
(
x
)
=
f
(
x
)
g
(
x
)
, then the local minimum value of the value of
h
(
x
)
is:
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