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KoMaL A Problems
KoMaL A Problems 2017/2018
A. 725
Functional challenge 4
Functional challenge 4
Source: Komal, 2018,june,A, 725
April 6, 2021
function
algebra
Problem Statement
Let
R
+
\mathbb R^+
R
+
denote the set of positive real numbers.Find all functions
f
:
R
+
→
R
+
f:\mathbb R^+\rightarrow \mathbb R^+
f
:
R
+
→
R
+
satisfying the following equation for all
x
,
y
∈
R
+
x,y\in \mathbb R^+
x
,
y
∈
R
+
:
f
(
x
y
+
f
(
y
)
2
)
=
f
(
x
)
f
(
y
)
+
y
f
(
y
)
f(xy+f(y)^2)=f(x)f(y)+yf(y)
f
(
x
y
+
f
(
y
)
2
)
=
f
(
x
)
f
(
y
)
+
y
f
(
y
)
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