Question 140
Consider the functions $f, g : \mathbb{R} \to \mathbb{R}$, such that $g(x) = 2f(x) + f(x^2)$, for all $x \in \mathbb{R}$.
a) Prove that if $f$ is locally bounded in the origin and $g$ is continuous in the origin, then $f$ is continuous in the origin.
b) Give an example of a function $f$, discontinuous in the origin, such that $g$ is continuous in the origin.
a) Prove that if $f$ is locally bounded in the origin and $g$ is continuous in the origin, then $f$ is continuous in the origin.
b) Give an example of a function $f$, discontinuous in the origin, such that $g$ is continuous in the origin.