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Mathematics
Problem
Let
f
:
R
→
R
f: R \to R
f
:
R
→
R
satisfy
f
(
x
+
y
)
=
2
x
f
(
y
)
+
4
y
f
(
x
)
,
∀
x
,
y
∈
R
.
If
f
(
2
)
=
3
,
f(x + y) = 2^{x} f(y) + 4^{y} f(x), \forall x, y \in R. \text{ If } f(2) = 3,
f
(
x
+
y
)
=
2
x
f
(
y
)
+
4
y
f
(
x
)
,
∀
x
,
y
∈
R
.
If
f
(
2
)
=
3
,
then
f
′
(
4
)
f
′
(
2
)
\frac{f'(4)}{f'(2)}
f
′
(
2
)
f
′
(
4
)
is equal to ...................................
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