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MAA AMC
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2018 USAMO
2
FEel the burn
FEel the burn
Source: 2018 USAMO 2
April 18, 2018
AMC
USA(J)MO
USAMO
function
2018 USAMO Problem 2
Hi
Problem Statement
Find all functions
f
:
(
0
,
∞
)
→
(
0
,
∞
)
f:(0,\infty) \rightarrow (0,\infty)
f
:
(
0
,
∞
)
→
(
0
,
∞
)
such that
f
(
x
+
1
y
)
+
f
(
y
+
1
z
)
+
f
(
z
+
1
x
)
=
1
f\left(x+\frac{1}{y}\right)+f\left(y+\frac{1}{z}\right) + f\left(z+\frac{1}{x}\right) = 1
f
(
x
+
y
1
)
+
f
(
y
+
z
1
)
+
f
(
z
+
x
1
)
=
1
for all
x
,
y
,
z
>
0
x,y,z >0
x
,
y
,
z
>
0
with
x
y
z
=
1
xyz =1
x
yz
=
1
.
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