Dirichlet defined a func. g into a piecewise function depending on whether the input $\displaystyle x$ is rational or not. That is:

$\displaystyle g(x) = 1\ \text{if}\ x \in \mathbb{Q} ... 0\ \text{if}\ x \notin \mathbb{Q}$

Using the same idea that Dirchlet did with his constructions, make a function on $\displaystyle \mathbb{R}$ such that it's diferentiable at a single point.