Find all functions $f:\mathbb{R}\to\mathbb{R}$ such that $$f(x+y)\leq f(x^2+y)$$for all $x,y$.
Source: Own, Romanian National MO 2019 Grade 9 P4
Tags: inequalities
Find all functions $f:\mathbb{R}\to\mathbb{R}$ such that $$f(x+y)\leq f(x^2+y)$$for all $x,y$.