Let $f,g:\mathbb{R}\longrightarrow\mathbb{R}$, and assume that $f$ is continuous from the right at $x_0$, and $g$ is continuous from the right at $f(x_0)$.
Is $g\circ f$ continuous from the right at $x_0$?
Intuitively I'm pretty sure this isn't neccessarly right, but I can't think about a counter example