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Byju's Answer
Standard XII
Mathematics
Domain
Find the doma...
Question
Find the domain of the function defined as
f
(
x
)
=
1
1
−
x
2
.
A
x
ϵ
R
−
{
1
,
−
1
}
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B
x
ϵ
R
−
{
0
}
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C
x
ϵ
R
−
{
−
1
}
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D
x
ϵ
R
−
{
1
}
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Solution
The correct option is
A
x
ϵ
R
−
{
1
,
−
1
}
f
(
x
)
=
1
1
−
x
2
For existance
1
−
x
2
≠
0
⇒
x
≠
+
1
,
−
1
⇒
x
∈
R
−
{
1
,
−
1
}
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0
Similar questions
Q.
Show that the function
f
:
R
→
{
x
ϵ
R
:
−
1
<
x
<
1
}
defined by
f
(
x
)
=
x
1
+
|
x
|
x
ϵ
R
is one one and onto function.
Q.
Let
f
(
x
)
=
x
2
−
1
,
x
ϵ
R
. Find
1
2
f
(
5
)
Q.
Let
f
(
x
)
=
x
2
−
1
,
x
ϵ
R
. Find
f
(
3
)
−
f
(
2
)
Q.
Consider the function
f
(
x
)
=
x
2
−
1
x
2
+
1
, where
x
ϵ
R
.
What is the minimum value of
f
(
x
)
?
Q.
Let
g
(
x
)
=
1
4
f
(
2
x
2
−
1
)
+
1
2
f
(
1
−
x
2
)
∀
x
ϵ
R
, where
f
′′
(
x
)
>
0
∀
x
ϵ
R
. g(x) is necessarily increasing in the interval
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