# Functions of bounded variation and $L^\infty$ functions

Here are my questions.

• Are $L^\infty$ functions of bounded variation?
• Is the composition of two BV functions still of bounded variation?
• Is $x\mapsto \frac 1{f(x)}$ of bounded variation when $f$ is of bounded variation?

Cheers.

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What do you think about these problems? – Davide Giraudo Oct 11 '12 at 12:28
Here are your answers: no, no, no. – Willie Wong Oct 11 '12 at 12:31

As said above: no, no, no. (1) Consider $\sin(1/x)$. (2) Consider $\sqrt{x}$ composed with $x^2\sin^2(1/x)$. (3) Consider $1/x$.