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Korea Junior Mathematics Olympiad
2017 Korea Junior Math Olympiad
7
No function satisfying the condition
No function satisfying the condition
Source: KJMO 2017 p7
July 26, 2019
algebra
KJMO
Problem Statement
Prove that there is no function
f
:
R
≥
0
→
R
f:\mathbb{R}_{\ge0}\rightarrow\mathbb{R}
f
:
R
≥
0
→
R
satisfying:
f
(
x
+
y
2
)
≥
f
(
x
)
+
y
f(x+y^2)\ge f(x)+y
f
(
x
+
y
2
)
≥
f
(
x
)
+
y
for all two nonnegative real numbers
x
,
y
x,y
x
,
y
.
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