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Mathematics
Mathematics
Problem
Let the function satisfy the equation
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
f(x+y) = f(x)f(y)
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
, where
f
(
0
)
≠
0
f(0) \neq 0
f
(
0
)
=
0
. If
f
(
5
)
=
3
f(5) = 3
f
(
5
)
=
3
and
f
′
(
0
)
=
2
f'(0) = 2
f
′
(
0
)
=
2
, then
f
′
(
5
)
f'(5)
f
′
(
5
)
is (a) 6 (b) 0 (c) 5 (d) -6
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