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Mathematics
Mathematics
Problem
Let
f
f
f
be differentiable function satisfying
f
(
x
y
)
=
f
(
x
)
−
f
(
y
)
f\left(\frac{x}{y}\right) = f(x) - f(y)
f
(
y
x
)
=
f
(
x
)
−
f
(
y
)
for all
x
,
y
>
0
x, y > 0
x
,
y
>
0
. If
f
′
(
1
)
=
1
f'(1) = 1
f
′
(
1
)
=
1
, then
f
(
x
)
f(x)
f
(
x
)
is a.
2
log
e
x
2 \log_e x
2
lo
g
e
x
b.
3
log
e
x
3 \log_e x
3
lo
g
e
x
c.
log
e
x
\log_e x
lo
g
e
x
d.
1
2
log
e
x
\frac{1}{2} \log_e x
2
1
lo
g
e
x
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