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Mathematics
Mathematics
Problem
If
f
(
x
y
)
=
f
(
x
)
f
(
y
)
f\left(\frac{x}{y}\right) = \frac{f(x)}{f(y)}
f
(
y
x
)
=
f
(
y
)
f
(
x
)
for all
x
,
y
∈
R
,
y
≠
0
x, y \in \mathbb{R}, y \neq 0
x
,
y
∈
R
,
y
=
0
and
f
′
(
x
)
f'(x)
f
′
(
x
)
exists for all
x
x
x
,
f
(
2
)
=
4
f(2) = 4
f
(
2
)
=
4
. Then,
f
(
5
)
f(5)
f
(
5
)
is a. 3 b. 5 c. 25 d. None of the above
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