Question

If $X\in R,$ then sgn $\left(X^2+1\right)$ is equal to

• A. $0$ or $-1$
• B. $0$
• C. $1$
• D. $-1$

Answer 1

The correct option is C $1$

We know that $sgn\left(x\right)=1forx>0$

$sgn\left(x\right)=0forx=0$

$sgn\left(x\right)=-1forx<0$

So, $sgn\left(x\right)=\frac{x}{|x|}$

$similarly,sgn(x^2+1)=\frac{(x^2+1)}{|x^2+1|}$

if x is real then $x^2+1>0$

therefore, $sgn(x^2+1)=1$