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JBMO TST - Turkey
2023 JBMO TST - Turkey
3
One variable function in Turkey JBMO TST
One variable function in Turkey JBMO TST
Source: Turkey JBMO TST 2023 Day 1 P3
April 30, 2023
function
algebra
Problem Statement
Find all
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that
f
(
x
+
f
(
x
)
)
=
f
(
−
x
)
f(x+f(x))=f(-x)
f
(
x
+
f
(
x
))
=
f
(
−
x
)
and for all
x
≤
y
x \leq y
x
≤
y
it satisfies
f
(
x
)
≤
f
(
y
)
f(x) \leq f(y)
f
(
x
)
≤
f
(
y
)
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