Prove that there is no function $f : \mathbb{R}^+ → \mathbb{R}^+$ such that $$f(x)^2 ≥ f(x + y)(f(x) + y)$$ for all $x, y > 0$.
I can't think of a way of solving this.
Prove that there is no function $f : \mathbb{R}^+ → \mathbb{R}^+$ such that $$f(x)^2 ≥ f(x + y)(f(x) + y)$$ for all $x, y > 0$.
I can't think of a way of solving this.