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2012 IMAC Arhimede
3
y=1/2 [f (x+y/x)- (f(x)+f(y)/f(x)}], functional in Q^+
y=1/2 [f (x+y/x)- (f(x)+f(y)/f(x)}], functional in Q^+
Source: IMAC Archimede 2012 p3
May 6, 2019
algebra
functional equation
functional equation in Q
Problem Statement
Find all functions
f
:
Q
+
→
Q
+
f:Q^+ \to Q^+
f
:
Q
+
→
Q
+
such that for any
x
,
y
∈
Q
+
x,y \in Q^+
x
,
y
∈
Q
+
:
y
=
1
2
[
f
(
x
+
y
x
)
−
(
f
(
x
)
+
f
(
y
)
f
(
x
)
)
]
y=\frac{1}{2}\left[f\left(x+\frac{y}{x}\right)- \left(f(x)+\frac{f(y)}{f(x)}\right)\right]
y
=
2
1
[
f
(
x
+
x
y
)
−
(
f
(
x
)
+
f
(
x
)
f
(
y
)
)
]
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