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Mathematics
Mathematics
Problem
If
f
(
x
)
f(x)
f
(
x
)
is a real-valued function discontinuous at all integral points lying in
[
0
,
n
]
[0, n]
[
0
,
n
]
and if
(
f
(
x
)
)
2
=
1
,
∀
x
∈
[
0
,
n
]
(f(x))^2 = 1, \forall x \in [0, n]
(
f
(
x
)
)
2
=
1
,
∀
x
∈
[
0
,
n
]
, then number of functions
f
(
x
)
f(x)
f
(
x
)
are a.
2
n
+
1
2^{n+1}
2
n
+
1
b.
6
×
3
n
6 \times 3^n
6
×
3
n
c.
2
×
3
n
−
1
2 \times 3^{n-1}
2
×
3
n
−
1
d.
3
n
+
1
3^{n+1}
3
n
+
1
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