Seja $f:\mathbb{R}\to \mathbb{R}$ tal que:$$f(x)=\{\begin{array}{ll}\frac{1}{x},& \text{se}x\text{ for racional},x\ne 0\\ -\frac{1}{x},& \text{se }x\text{ for irracional}\\ 0,& \text{ se }x=0\end{array}$$

Seja $f^{+}:\mathbb{R}\to \mathbb{R}$ tal que: $$f^{+}(x)=\{\begin{array}{ll}f(x),& \text{se}f(x)>0\\ 0,& \text{se}f(x)\le 0\end{array}$$

Seja $f^{-}:\mathbb{R}\to \mathbb{R}$ tal que: $$f^{-}(x)=\{\begin{array}{ll}f(x),& \text{se}f(x)<0\\ 0,& \text{se}f(x)\ge 0\end{array}$$