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JEE Main Math Class 12 Application of Derivatives Part 1 Questions
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© examsnet.com
Question : 4
Total: 100
If the function
f
:
R
−
{
1
,
−
1
}
→
A
defined by
f
(
x
)
=
x
2
1
−
x
2
,
is surjective, then
A
is equal to:
[April 09, 2019 (I)]
R
−
{
−
1
}
[
0
,
"
)
R
−
[
−
1
,
0
)
R
−
(
−
1
,
0
)
Validate
Solution:
f
(
x
)
=
x
2
1
−
x
2
⇒
f
(
−
x
)
=
x
2
1
−
x
2
=
f
(
x
)
f
′
(
−
x
)
=
2
x
(
1
−
x
2
)
2
f
(
x
)
increases in
x
∈
(
10
,
∞
)
Also
f
(
0
)
=
0
and
lim
x
→
±
∞
f
(
x
)
=
−
1
and
f
(
x
)
is even function
Set
A
=
R
−
[
−
1
,
0
)
And the graph of function
f
(
x
)
is
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