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Problem
Problem
Let
f
:
R
→
R
f: R \rightarrow R
f
:
R
→
R
be a continuous onto function satisfying
f
(
x
)
+
f
(
−
x
)
=
0
,
∀
x
∈
R
f(x) + f(-x) = 0, \forall x \in R
f
(
x
)
+
f
(
−
x
)
=
0
,
∀
x
∈
R
. If
f
(
−
3
)
=
2
f(-3) = 2
f
(
−
3
)
=
2
and
f
(
5
)
=
4
f(5) = 4
f
(
5
)
=
4
in
[
−
5
,
5
]
[-5, 5]
[
−
5
,
5
]
then the equation
f
(
x
)
=
0
f(x) = 0
f
(
x
)
=
0
has (a) exactly three real roots (b) exactly two real roots (c) atleast five real roots (d) atleast three real roots
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