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2
2018 PUMaC Individual Finals A2
2018 PUMaC Individual Finals A2
Source:
January 8, 2019
function
PuMAC
Individual Finals
Problem Statement
Find all functions
f
:
R
+
→
R
+
f:\mathbb{R^{+}}\to\mathbb{R^+}
f
:
R
+
→
R
+
such that for all
x
,
y
∈
R
+
x,y\in\mathbb{R^+}
x
,
y
∈
R
+
it holds that
f
(
x
y
(
1
x
+
1
y
+
1
x
+
y
)
)
=
f
(
x
y
(
1
x
+
1
y
)
)
+
f
(
x
)
f
(
y
x
+
y
)
.
f\left(xy\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{x+y}\right)\right)=f\left(xy\left(\frac{1}{x}+\frac{1}{y}\right)\right)+f(x)f\left(\frac{y}{x+y}\right).
f
(
x
y
(
x
1
+
y
1
+
x
+
y
1
)
)
=
f
(
x
y
(
x
1
+
y
1
)
)
+
f
(
x
)
f
(
x
+
y
y
)
.
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