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Iran-Singapore-Taiwan Friendly Math Competition
2022 Iran-Taiwan Friendly Math Competition
2
2
Part of
2022 Iran-Taiwan Friendly Math Competition
Problems
(1)
Function using maximum
Source: 2022 IRN TWN Friendly math competition P2
6/23/2022
Find all functions
f
:
R
→
R
f:\mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that:
∙
\bullet
∙
f
(
x
)
<
2
f(x)<2
f
(
x
)
<
2
for all
x
∈
(
0
,
1
)
x\in (0,1)
x
∈
(
0
,
1
)
;
∙
\bullet
∙
for all real numbers
x
,
y
x,y
x
,
y
we have:
m
a
x
{
f
(
x
+
y
)
,
f
(
x
−
y
)
}
=
f
(
x
)
+
f
(
y
)
max\{f(x+y),f(x-y)\}=f(x)+f(y)
ma
x
{
f
(
x
+
y
)
,
f
(
x
−
y
)}
=
f
(
x
)
+
f
(
y
)
Proposed by Navid Safaei
algebra
functional equation
function
Taiwan
Iran