Question

Two functions $f:R\to R,g:R\to R$ are defined as follows $f\left(x\right)=\{\begin{array}{cc}0,& x\in Q\\ 1,& x\notin Q\end{array}$, $g\left(x\right)=\{\begin{array}{cc}-1& x\in Q\\ 0,& x\notin Q\end{array}$, then $g\left(f\right(e\left)\right)+f\left(g\right(\pi \left)\right)=$

• A. $0$
• B. $-1$
• C. $1$
• D. $2$

Answer 1

The correct option is B $-1$

$\begin{array}{cc}g\left(f\right(e\left)\right)+f\left(g\right(\pi \left)\right)& =g\left(1\right)+f\left(0\right)\\ & =-1+0=-1\end{array}$