Question

If $x-0.5=\text{sgn}\left(x\right),$ then the possible value(s) of $x$ is/are
(where $\text{sgn}\left(x\right)$ denotes the signum function)

• A. $0.5$
• B. $-0.5$
• C. $1.5$
• D. $-1.5$

Answer 1

Answer: (B), (C)

$1.5$

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

Now,
When $x>0$, we get
$x-0.5=1\Rightarrow x=1.5$

When $x=0$, we get
$0-0.5=0\Rightarrow -0.5=0\text{(not possible)}$

When $x<0$
$x-0.5=-1\Rightarrow x=-0.5$