Y by
Show that there does not exist a function
![\[
f : \mathbb{R}^+ \to \mathbb{R}
\]](//latex.artofproblemsolving.com/e/7/b/e7bfc5b236fb6f00ef328f850b1b14632cbf8416.png)
satisfying the condition that for all 
,
![\[
f(x + y^2) \geq f(x) + y.
\]](//latex.artofproblemsolving.com/3/a/a/3aa20083835682dbd81be692eba65cab19e923e5.png)
~Korea 2017 P7
![\[
f : \mathbb{R}^+ \to \mathbb{R}
\]](http://latex.artofproblemsolving.com/e/7/b/e7bfc5b236fb6f00ef328f850b1b14632cbf8416.png)
satisfying the condition that for all 
,![\[
f(x + y^2) \geq f(x) + y.
\]](http://latex.artofproblemsolving.com/3/a/a/3aa20083835682dbd81be692eba65cab19e923e5.png)
~Korea 2017 P7
This post has been edited 3 times. Last edited by Jackson0423, Apr 21, 2025, 3:23 PM
Reason: Sorry guys..
Reason: Sorry guys..
is the set of nonnegative integers
and 
?
is not always true. Check 
.
and 
.
for all positive integers 
.
,
,![\[f(x+1)\ge f(x)+N\]](http://latex.artofproblemsolving.com/e/6/d/e6d7a6bcac7cb561489adbf005fd4c784afac66d.png)
so 
is infinitely large, contradiction.
