Let $$X$$ be a subset of $$\mathbb{R}$$, let $$f : X \to \mathbb{R}$$ and $$g : X \to \mathbb{R}$$ be functions, and let $$x_0$$ be an element of $$X$$. Then, if $$f$$ and $$g$$ are continuous at $$x_0$$, then so too are the functions [...], [...], [...], [...] and [...]. If $$g$$ is non-zero on $$X$$, then [...] is also continuous at $$x_0$$.