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Problem
Problem
If
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
f(x+y) = f(x)f(y)
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
and
∑
x
=
1
∞
f
(
x
)
=
2
,
x
,
y
∈
N
\sum_{x=1}^{\infty} f(x) = 2, x, y \in N
∑
x
=
1
∞
f
(
x
)
=
2
,
x
,
y
∈
N
where
N
N
N
is the set of all natural numbers, then the value of
f
(
4
)
f
(
2
)
\frac{f(4)}{f(2)}
f
(
2
)
f
(
4
)
is (a)
1
9
\frac{1}{9}
9
1
(b)
4
9
\frac{4}{9}
9
4
(c)
1
3
\frac{1}{3}
3
1
(d)
2
3
\frac{2}{3}
3
2
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