MathDB
Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch IMO TST
2018 Dutch IMO TST
2
f(x^2) - f(y^2) <= (f(x)+y) (x-f(y))
f(x^2) - f(y^2) <= (f(x)+y) (x-f(y))
Source: Dutch IMO TST day 3 p2
August 30, 2019
Functional inequality
function
inequalities
algebra
Problem Statement
Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that
f
(
x
2
)
−
f
(
y
2
)
≤
(
f
(
x
)
+
y
)
(
x
−
f
(
y
)
)
f(x^2)-f(y^2) \le (f(x)+y) (x-f(y))
f
(
x
2
)
−
f
(
y
2
)
≤
(
f
(
x
)
+
y
)
(
x
−
f
(
y
))
for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
.
Back to Problems
View on AoPS