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2016 CIIM
Problem 1
Problem 1
Part of
2016 CIIM
Problems
(1)
CIIM 2016 Problem 1
Source:
10/18/2017
Find all functions
f
:
(
0
,
+
∞
)
→
(
0
,
+
∞
)
f:(0,+\infty) \to (0,+\infty)
f
:
(
0
,
+
∞
)
→
(
0
,
+
∞
)
that satisfy
(
i
)
(i)
(
i
)
f
(
x
f
(
y
)
)
=
y
f
(
x
)
,
∀
x
,
y
>
0
,
f(xf(y))=yf(x), \forall x,y > 0,
f
(
x
f
(
y
))
=
y
f
(
x
)
,
∀
x
,
y
>
0
,
(
i
i
)
(ii)
(
ii
)
lim
x
→
+
∞
f
(
x
)
=
0.
\displaystyle\lim_{x\to+\infty} f(x) = 0.
x
→
+
∞
lim
f
(
x
)
=
0.
CIIM
function