MathDB
Problems
Contests
National and Regional Contests
Iran Contests
Iran Team Selection Test
2013 Iran Team Selection Test
9
functional equation
functional equation
Source: Iran TST 2013:TST 2,Day 1,Problem 3
April 23, 2013
function
algebra proposed
algebra
Problem Statement
find all functions
f
,
g
:
R
+
→
R
+
f,g:\mathbb{R}^{+} \rightarrow \mathbb{R}^{+}
f
,
g
:
R
+
→
R
+
such that
f
f
f
is increasing and also:
f
(
f
(
x
)
+
2
g
(
x
)
+
3
f
(
y
)
)
=
g
(
x
)
+
2
f
(
x
)
+
3
g
(
y
)
f(f(x)+2g(x)+3f(y))=g(x)+2f(x)+3g(y)
f
(
f
(
x
)
+
2
g
(
x
)
+
3
f
(
y
))
=
g
(
x
)
+
2
f
(
x
)
+
3
g
(
y
)
g
(
f
(
x
)
+
y
+
g
(
y
)
)
=
2
x
−
g
(
x
)
+
f
(
y
)
+
y
g(f(x)+y+g(y))=2x-g(x)+f(y)+y
g
(
f
(
x
)
+
y
+
g
(
y
))
=
2
x
−
g
(
x
)
+
f
(
y
)
+
y
Back to Problems
View on AoPS