Question

The number of values of $x$ satisfying the equation $1+x=\text{sgn}\left(x\right)$ is
(where $\text{sgn}\left(x\right)$ denotes the signum function)

Answer 1

$\text{sgn}\left(x\right)=\{\begin{array}{cc}-1,& x<0\\ 0,& x=0\\ 1,& x>0\end{array}$

Now,
If $x>0,1+x=1\Rightarrow x=0\text{(rejected)}$
If $x=0,1+x=0\Rightarrow x=-1\text{(rejected)}$
If $x<0,1+x=-1\Rightarrow x=-2$