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Question
Mathematics
Let f(x) be a function such that f(x+y)=f(x) ⋅ f(y) for all x, y ∈ N. If f(1)=3 and displaystyle∑k=1n f(k)=3279, then the value of n is
Q. Let
f
(
x
)
be a function such that
f
(
x
+
y
)
=
f
(
x
)
⋅
f
(
y
)
for all
x
,
y
∈
N. If
f
(
1
)
=
3
and
k
=
1
∑
n
f
(
k
)
=
3279
, then the value of
n
is
287
152
JEE Main
JEE Main 2023
Relations and Functions
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A
8
11%
B
6
20%
C
7
51%
D
9
18%
Solution:
f
(
x
+
y
)
=
f
(
x
)
⋅
f
(
y
)
∀
x
,
y
∈
N
,
f
(
1
)
=
3
f
(
2
)
=
f
2
(
1
)
=
3
2
f
(
3
)
=
f
(
1
)
f
(
2
)
=
3
3
f
(
4
)
=
3
4
f
(
k
)
=
3
k
k
=
1
∑
n
f
(
k
)
=
3279
f
(
1
)
+
f
(
2
)
+
f
(
3
)
+
………
+
f
(
k
)
=
3279
3
+
3
2
+
3
3
+
………
3
k
=
3279
3
−
1
3
(
3
k
−
1
)
=
3279
2
3
k
−
1
=
1093
3
k
−
1
=
2186
3
k
=
2187
k
=
7