Question 125
Let $f, g : \mathbb{R}^+ \to \mathbb{R}^+$ be two functions such that for all positive real numbers $x$ and $y$
$$
f(x + g(y))^2 = f(x^2) + y^2.
$$
Prove that the range of $g$ is not bounded from above.
$$
f(x + g(y))^2 = f(x^2) + y^2.
$$
Prove that the range of $g$ is not bounded from above.