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Albania IMO TST functional equation
Albania IMO TST functional equation
Source:
May 18, 2013
function
algebra
functional equation
Problem Statement
Let
f
:
R
+
→
R
+
f:\mathbb R^+ \to \mathbb R^+
f
:
R
+
→
R
+
be a function such that:
x
,
y
>
0
f
(
x
+
f
(
y
)
)
=
y
f
(
x
y
+
1
)
.
x,y > 0 \qquad f(x+f(y)) = yf(xy+1).
x
,
y
>
0
f
(
x
+
f
(
y
))
=
y
f
(
x
y
+
1
)
.
a) Show that
(
y
−
1
)
∗
(
f
(
y
)
−
1
)
≤
0
(y-1)*(f(y)-1) \le 0
(
y
−
1
)
∗
(
f
(
y
)
−
1
)
≤
0
for
y
>
0
y>0
y
>
0
. b) Find all such functions that require the given condition.
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