Define $f: R\to R$ by $f\left(x\right)=\max \{x+1, 1-x, 2\}.$ Then $f$ is $\_\_\_$

Two functions $f:R\to R$ and $g:R\to R$ are defined as follows:

$f\left(x\right)=\left\{\begin{array}{l}0; \left(x\mathrm{rational}\right)\\ 1; \left(x\mathrm{irrational}\right)\end{array}\right.$

$g\left(x\right)=\left\{\begin{array}{l}-1; \left(x\mathrm{rational}\right)\\ 0; \left(x\mathrm{irrational}\right)\end{array}\right.$

then $\left(gof\right)\left(e\right)+\left(fog\right)\left(\pi \right)=$