# Prove or find a counter example to those statements.

Let the funktions $f,g:\mathbb{R} \rightarrow \mathbb{R}$ and $a\in\mathbb{R}$.

a) $f$ is continuos in $a$ $\Leftrightarrow$ $|f|$ is continuos in a;

b) $f,g$ are continuos in $a$ $\Rightarrow$ $max\{f,g\}$ and $min\{f,g\}$ are continuos in $a$;

c) $f,g$ are continuos in $a$ $\Leftrightarrow$ $f \cdot g$ is continuos in $a$.

• What are your thoughts? Hint: all claimed $\Leftarrow$ are false with simple counterexmples – Hagen von Eitzen Nov 20 '15 at 12:46
(a) You may use the $\delta$-$\epsilon$ definition of continuity, the reverse triangle inequality.