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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

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    Suggestion: take a function $g$ which is *not* continuous from the left at $f(x_0)$, and make $f$ decreasing.2012-01-23

2 Answers 2