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Standard XII
Mathematics
Question
Let
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
for all x and y. If
f
(
5
)
=
2
and
f
′
(
0
)
=
3
then
f
′
(
5
)
is equal to
5
8
6
12
A
6
B
5
C
8
D
12
Open in App
Solution
Verified by Toppr
f
(
x
+
h
)
=
f
(
x
)
f
(
h
)
Putting
x
=
0
,
y
=
5
in the given equation, we get
f
(
0
+
5
)
=
f
(
0
)
f
(
5
)
⟹
f
(
5
)
[
f
(
0
)
−
1
]
=
0
⟹
f
(
0
)
=
1
Consider,
f
′
(
5
)
=
lim
h
→
0
f
(
5
+
h
)
−
f
(
5
)
h
=
lim
h
→
0
f
(
5
)
f
(
h
)
−
f
(
5
)
h
=
lim
h
→
0
f
(
5
)
[
f
(
h
)
−
1
]
h
=
f
(
5
)
lim
h
→
0
f
(
h
)
−
f
(
0
)
h
=
f
(
5
)
f
′
(
0
)
=
2
×
3
=
6
∴
f
′
(
5
)
=
6
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If
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