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2015 Turkey Junior National Olympiad
1
1
Part of
2015 Turkey Junior National Olympiad
Problems
(1)
Functional inequality
Source: 2015 Turkey Junior National Olympiad P1
12/7/2015
For a non-constant function
f
:
R
ā
R
f:\mathbb{R}\to \mathbb{R}
f
:
R
ā
R
prove that there exist real numbers
x
,
y
x,y
x
,
y
satisfying
f
(
x
+
y
)
<
f
(
x
y
)
f(x+y)<f(xy)
f
(
x
+
y
)
<
f
(
x
y
)
function